Apparatus and method for generating audio subband values and apparatus and method for generating time-domain audio samples
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- 1Zastrzeżenia patentowe 1. Urządzenie do generowania wartości podpasm audio o wartościach zespolonych w kanałach podpasm audio, zawierające:moduł (110) okienkowania analizy do okienkowania ramki (120) wejściowych próbek audio w dziedzinie czasu będących w sekwencji czasu rozciągającej się od próbki wczesnej do próbki późniejszej z wykorzystaniem funkcji (190) okna analizy zawierającej sekwencję współczynników okna dla uzyskania okienkowanych próbek, przy czym funkcja (190) okna analizy zawiera pierwszą grupę (200) współczynników okna, zawierającą pierwszą część sekwencji współczynników okna i drugą grupę (210) współczynników okna, zawierającą drugą część sekwencji współczynników okna, przy czym pierwsza część zawiera mniej współczynników okna niż druga część, przy czym wartość energii całkowitej współczynników okna w pierwszej części jest większa od wartości energii całkowitej współczynników okna drugiej części, przy czym pierwsza grupa współczynników okna jest wykorzystywana do okienkowania późniejszych próbek w dziedzinie czasu, a druga grupa współczynników okna jest wykorzystywana do okienkowania wcześniejszych próbek w dziedzinie czasu, przy czym moduł okienkowania analizy jest przystosowany do działania w oparciu o równanie: z i n = w(10W - 1 - n) · dla θ - 11 io · w, przy czym zi,n jest okienkowaną próbką o wartościach rzeczywistych odpowiadającą indeksowi i bloku oraz indeksowi n próbki ramki, przy czym xi,n jest wejściową próbką audio o wartościach rzeczywistych w dziedzinie czasu odpowiadającą indeksowi i bloku oraz indeksowi n próbki, przy czym w zawiera współczynniki okna o wartościach rzeczywistych funkcji okna analizy i przy czym N jest parametrem wskazującym na liczbę próbek w bloku;i kalkulator (170) do obliczania wartości podpasm audio z wykorzystaniem okienkowanych próbek, przy czym kalkulator (170) zawiera przetwornik czasowo-częstotliwościowy przystosowany do generowania wartości podpasm audio w taki sposób, że wszystkie wartości podpasm na podstawie jednej ramki (150) okienkowanych próbek reprezentują reprezentację widmową okienkowanych próbek ramki (150) okienkowanych próbek, i 109 przy czym przetwornik czasowo-częstotliwościowy jest przystosowany do generowania wartości podpasm audio o wartościach zespolonych, i przy czym kalkulator jest przystosowany do działania w oparciu o równania: przy czym indeks współczynnika widmowego lub indeks k pasma jest liczbą całkowitą w zakresie 0 k N, przy czym XReai,i,k and Ximag,i,k reprezentują część rzeczywistą i część urojoną wartości podpasm audio o wartościach zespolonych odpowiadającej indeksowi i bioku oraz indeksowi k widmowemu i przy czym n0 jest parametrem reprezentującym opcję indeksu, i przy czym urządzeniem do generowania wartości podpasm audio o wartościach zespoionych w kanałach podpasm audio jest bank fiitrów anaiizy. 2. Urządzenie (300) do generowania próbek audio o wartościach rzeczywistych w dziedzinie czasu, zawierające: kaikuiator (310) do obiiczania sekwencji (330) pośrednich próbek w dziedzinie czasu z wartości podpasm audio w kanałach podpasm audio, przy czym sekwencja zawiera wcześniejsze pośrednie próbki w dziedzinie czasu i późniejsze pośrednie próbki w dziedzinie czasu, przy czym kaikuiator (310) zawiera przetwornik częstotiiwościowo-czasowy przystosowany do generowania sekwencji pośrednich próbek w dziedzinie czasu w taki sposób, że wartości podpasm audio dostarczane do kaikuiatora (310) reprezentują reprezentację widmową sekwencji pośrednich próbek w dziedzinie czasu, i przy czym przetwornik częstotiiwościowo-czasowy jest przystosowany do generowania sekwencji pośrednich próbek w dziedzinie czasu na podstawie wartości podpasm audio o wartościach zespoionych;przy czym kaikuiator jest przystosowany do działania w oparciu o równanie: ł,n N dia 0 n 10 N, przy czym x'i,n jest pośrednią próbką w dziedzinie czasu ramki odpowiadającej indeksowi n próbki oraz indeksowi i bioku, przy czym N jest iiczbą całkowitą wskazującą długość bioku, przy czym XReai,i,k i Ximag,i,k reprezentują część rzeczywistą i część urojoną wartości podpasm audio o wartościach zespoionych odpowiadającej indeksowi i bioku oraz indeksowi k współczynnika widmowego, przy czym n0 jest parametrem reprezentującym opcję indeksu, i przy czym N jest parametrem wskazującym iiczbę próbek w bioku;110 moduł (360) okienkowania syntezy do okienkowania sekwencji (330) pośrednich próbek w dziedzinie czasu z wykorzystaniem funkcji (370) okna syntezy zawierającej sekwencję współczynników okna dla uzyskania okienkowanych pośrednich próbek w dziedzinie czasu, przy czym funkcja (370) okna syntezy zawiera pierwszą grupę (420) współczynników okna zawierającą pierwszą część sekwencji współczynników okna i drugą grupę (430) współczynników okna zawierającą drugą część sekwencji współczynników okna, przy czym pierwsza część zawiera mniej współczynników okna niż druga część, przy czym wartość energii całkowitej współczynników okna w pierwszej części jest wyższa od wartości energii całkowitej współczynników okna drugiej części, przy czym pierwsza grupa współczynników okna jest wykorzystywana do okienkowania późniejszych pośrednich próbek w dziedzinie czasu, a druga grupa współczynników okna jest wykorzystywana do okienkowania wcześniejszych pośrednich próbek w dziedzinie czasu, przy czym moduł okienkowania syntezy jest przystosowany do działania w oparciu o równanie: z 'i,n = x'. O n 10 · N ι · η dla przy czym z'i,n jest wartością okienkowanej pośredniej próbki w dziedzinie czasu odpowiadającej indeksowi n próbki oraz indeksowi i bloku ramki, i przy czym w(n) są współczynnikami okna o wartościach rzeczywistych funkcji okna syntezy;i stadium (400) wyjściowe modułu dodawania z zakładką do przetwarzania okienkowanych pośrednich próbek w dziedzinie czasu dla uzyskania próbek w dziedzinie czasu, przy czym stadium wyjściowe modułu dodawania z zakładką jest przystosowane do działania w oparciu o równanie: ° U ^i.n ~ 2 i,n +Z i-\,n+N+ Z i-2,ii + 2N+ Z i-3.n+3N+ Z i-4,n+4N +Z i-Sji+SN + 2 i-f ,n + 6N +Z i-7,n+2N+ Z ί-8,ιι+$Ν + Z i-9,n+9N ’ dla 0 n N przy czym outi,n reprezentuje próbkę o wartościach rzeczywistych w dziedzinie czasu odpowiadającą indeksowi n próbki oraz indeksowi i bloku, i przy czym urządzeniem do generowania próbek audio o wartościach rzeczywistych w dziedzinie czasu jest bank filtrów syntezy. 3. Sposób generowania wartości podpasm audio o wartościach zespolonych w kanałach podpasm audio, obejmujący: okienkowanie ramki wejściowych próbek audio w dziedzinie czasu będących w sekwencji czasu rozciągającej się od próbki wczesnej do próbki późniejszej z wykorzystaniem funkcji okna analizy zawierającej pierwszą grupę (200) współczynników okna zawierającą pierwszą część sekwencji współczynników okna i drugą grupę (210) współczynników okna zawierającą drugą część sekwencji współczynników okna, przy czym pierwsza część zawiera mniej współczynników okna niż druga część, 111 przy czym wartość energii całkowitej współczynników okna w pierwszej części jest wyższa od wartości energii całkowitej współczynników okna drugiej części, przy czym pierwsza grupa (200) współczynników okna jest wykorzystywana do okienkowania późniejszych próbek w dziedzinie czasu, a druga grupa (210) współczynników okna jest wykorzystywana do okienkowania wcześniejszych próbek w dziedzinie czasu, przy czym okienkowanie opiera się na równaniu: z i n = w(10W - 1 - n) · x iitt dl a 0 - n 10 ' N ' przy czym zi,n jest okienkowaną próbką o wartościach rzeczywistych odpowiadającą indeksowi i bloku oraz indeksowi n próbki ramki, przy czym xi,n jest wejściową próbką audio o wartościach rzeczywistych w dziedzinie czasu odpowiadającą indeksowi i bloku oraz indeksowi n próbki, przy czym w zawiera współczynniki okna o wartościach rzeczywistych funkcji okna analizy i przy czym N jest parametrem wskazującym liczbę próbek w bloku, obliczanie wartości podpasm audio z wykorzystaniem okienkowanych próbek, przy czym obliczanie zawiera przetwarzanie czasowo-częstotliwościowe wartości podpasm audio w taki sposób, że wszystkie wartości podpasm na podstawie jednej ramki (150) okienkowanych próbek reprezentują reprezentację widmową okienkowanych próbek ramki (150) okienkowanych próbek, i przy czym przetwarzanie czasowo-częstotliwościowe wartości podpasm audio zawiera generowanie sekwencji pośrednich próbek w dziedzinie czasu na podstawie wartości podpasm audio o wartościach zespolonych, i przy czym obliczanie opiera się na równaniach: x ^ n ,.-, k = 2 Σ c ° s (^(«+ An^ 2 ' Σ + ' przy czym indeks współczynnika widmowego lub indeks k pasma jest liczbą całkowitą w zakresie 0 k N, przy czym XReai,i,k and Ximag,i,k reprezentują część rzeczywistą i część urojoną wartości podpasma o wartościach zespolonych odpowiadającej indeksowi i bloku oraz indeksowi k widmowemu, i przy czym n0 jest parametrem reprezentującym opcję indeksu, i przy czym sposób generowania wartości podpasm audio o wartościach zespolonych w kanałach podpasm audio jest realizowany przez bank filtrów analizy. 4. Sposób generowania próbek audio o wartościach rzeczywistych w dziedzinie czasu, obejmujący: 112 obiiczanie sekwencji pośrednich próbek w dziedzinie czasu z wartości podpasm audio w kanałach podpasm audio, przy czym sekwencja zawiera wcześniejsze pośrednie próbki w dziedzinie czasu i późniejsze pośrednie próbki w dziedzinie czasu, przy czym obiiczanie zawiera przetwarzanie częstotiiwościowo-czasowe wartości podpasm audio w taki sposób, że wartości podpasm audio reprezentują reprezentację widmową sekwencji pośrednich próbek w dziedzinie czasu;i przy czym przetwarzanie częstotiiwościowo-czasowe zawiera generowanie sekwencji pośrednich próbek w dziedzinie czasu na podstawie wartości podpasm audio o wartościach zespoionych;przy czym obiiczanie opiera się na równaniu: "tf-l ( „ f 1 \λ Λ'-Ι X '· Λί Σ* A=0 Ren/,/.A t COSI ~ (n + n 0 )( k + i I + Σ X I.W.Usin (« + 'M k + A=0 dia 0 n 10 N, przy czym x'i,n jest pośrednią próbką w dziedzinie czasu ramki odpowiadającej indeksowi n próbki oraz indeksowi i bioku, przy czym N jest iiczbą całkowitą wskazującą długość bioku, przy czym XReai,i,k and Ximag,i,k reprezentują część rzeczywistą i część urojoną wartości podpasm audio o wartościach zespoionych odpowiadającej indeksowi i bioku oraz indeksowi k współczynnika widmowego, i przy czym n0 jest parametrem reprezentującym opcję indeksu, i przy czym N jest parametrem wskazującym iiczbę próbek w bioku;okienkowanie sekwencji pośrednich próbek w dziedzinie czasu z wykorzystaniem funkcji okna syntezy zawierającej sekwencję współczynników okna dia uzyskania okienkowanych pośrednich próbek w dziedzinie czasu, przy czym funkcja okna syntezy zawiera pierwszą grupę (420) współczynników okna zawierającą pierwszą część sekwencji współczynników okna i drugą grupę (430) współczynników okna zawierającą drugą część sekwencji współczynników okna, przy czym pierwsza część zawiera mniej współczynników okna niż druga część, przy czym wartość energii całkowitej współczynnika okna w pierwszej części jest wyższa od wartości energii całkowitej współczynnika okna drugiej części, przy czym pierwsza grupa współczynników okna jest wykorzystywana do okienkowania późniejszych pośrednich próbek w dziedzinie czasu, a druga grupa (420) współczynników okna jest wykorzystywana do okienkowania wcześniejszych pośrednich próbek w dziedzinie czasu, przy czym okienkowanie opiera się na równaniu: z \,„ = ^(n) · x' i)nd|a ° n 10 · W, przy czym z'i,n jest wartością okienkowanej pośredniej próbki w dziedzinie czasu odpowiadającej indeksowi n próbki oraz indeksowi i bioku ramki, i przy czym w(n) są współczynnikami okna o wartościach rzeczywistych funkcji okna syntezy;i 113 dodawanie z zakładką okienkowanych próbek w dziedzinie czasu dla uzyskania próbek w dziedzinie czasu, przy czym dodawanie z zakładką opiera się na równaniu: OUt i lt = Z l n +Z ;_| η+λ ,+ Z i-2,u + 2N +Z i-l,ii+3N +Z ,-4.,,+4// +Z i-S,,i+SN + 2 i-f ,n + 6N +Z ί-Τ,η+ΊN+ Z ί-8,ιι+$Ν + Z i-9,n+9N ’ dla 0 n N przy czym outi,n reprezentuje próbkę o wartościach rzeczywistych w dziedzinie czasu odpowiadającą indeksowi n próbki oraz indeksowi i bloku, i przy czym sposób generowania próbek audio o wartościach rzeczywistych w dziedzinie czasu jest realizowany przez bank filtrów syntezy. 5. Program z kodem programu do wykonywania, gdy jest uruchomiony na procesorze, sposobu określonego w zastrz. 3 albo określonego w zastrz. 4. Fraunhofer Gesellschaft zur Forderung der angewandten Forschung e. V., Niemcy Pełnomocnik: 114 1/29 EP 2 076 901 B1 Z-15889/17 FIG 1 100 220 180 115 EP 2 076 901 B1 2/29 Z-15889/17 116 EP 2 076 901 B1 3/29 Z-15889/17 117 EP 2 076 901 B1 4/29 Z-15889/17 118 EP 2 076 901 B1 5/29 Z-15889/17 FIG 5 500 σ ro co 119 520 IN I Ul CO "O ro o \i σι co o oo NI FIG 6 ro eo 120 IN I Ul LD "O ro o NI σ LD o NI 121 EP 2 076 901 B1 8/29 Z-15889/17 FIG7A 122 EP 2 076 901 B1 9/29 Z-15889/17 123 EP 2 076 901 B1 10/29 Z-15889/17 FIG7C 124 EP 2 076 901 B1 11/29 Z-15889/17 FIG 8A 125 EP 2 076 901 B1 12/29 Z-15889/17 FIG 8B 126 EP 2 076 901 B1 13/29 Z-15889/17 FIG 8C Koniec S370 127 EP 2 076 901 B1 14/29 Z-15889/17 FIG 8D 128 EP 2 076 901 B1 15/29 Z-15889/17 FIG 9A S400 S410 S420 S430 S440 S450 S460 S470 S480 function [y, State] = tdfb80 (x, State) % aktualizuj bufor State (640-64+(1:64)) = x;% zastosuj okno win_ana = ldfb80_win;% załóż, że ostatnie próbki są ułożone z prawej strony bufora x_win_orig = State. *win_ana;% przygotuj stos x_stack = reshape (x_win_orig, 128,5);% podpisz zmianę . x_stack(: ,2:2:4)) = -x_stack(:,(2:2:4));% zwiń stos 'x_stack = sum(-x_stack(end:-1:1,:),2)’;o/ Q nieparzyste FFT okienkowanych danych temp = fft(x_stack.*exp(-1i*pi*(0:128-1)/128));% publikuj fazę .m = (64+1)/2 y = 2*conj (temp (1:64) ?exp(-2i*pi* ((0:64-1 )+0.5)*m/128));% zmień bufor State (1:640-64) = State (64+(1:640-64));129 EP 2 076 901 B1 16/29 Z-15889/17 FIG 9B function [y, State] = ldfb80_32 (x, State) % | aktualizuj bufor S State (320-32+(1:32)) = x;% zastosuj okno win_ana = ldfb80_win();win_ana = (win_ana (1:2:end) + win_ana (2:2:end))/2;% załóż, że ostatnie próbki są ułożone z prawej strony bufora x_win_orig = State. *win_ana;% przygotuj stos x_stack = reshape (x_win_orig,64,5);podpisz zmianę x_stack(:, (2:2:4)) = -x_stack(:,(2:2:4));'o/ Ql zwiń stos x_stack = sum(-x_stack(end:-1:1 ,:),2)’;% | nieparzyste FFT okienkowanych danych temp = fft( x_stack.*exp(-1 i*pi*(0:64-1 )/64));% | publikuj fazę m = (32+1)/2 $480* y = 2*conj (temp (1:32) .*exp(-2i*pi*((0:32-1)+0.5)*m/64));% zmień bufor State (1:320-32) = State (32+(1:320-32)): S400’ S412 S420 S430’ S440 S450 S460’ 130 EP 2 076 901 B1 Z-15889/17 17/29 FIG10A S500 S510 S520 S530 S540 S550 S560 S570 S580 function [y, State] = Fdfb80 (x, State) % wstępne fazowanie "m = (64+1)/2: . temp = 0.5*conj (x).*exp( (2i*pi*((0:64-1 )+0.5)*m/128));% nieparzysta symetria "temp = [temp conj (temp (64:-1:1))];% nieparzyste FFT y_knl = real (ifft (temp) .* exp(i*pi*(0:128-1)/128));% rozszerz dane;zmień znak przełączenia y knl = -y_knl (128:-1:1);tmp = [y_knl -y_knl y_knl -y_knl y_knl]’;% okno syntezy win_ana = ldfb80_win;win_syn = win_ana(end:-1:1);% zastosuj okno 'tmp = tmp.*win_sys;% aktualizuj bufor .State (640-64+(1:64)) = 0;state = stałe + tmp;% pozyskaj wyjście y = state(1:64);% zmień bufor State (1:640-64) = State (64+1:640);131 EP 2 076 901 B1 18/29 Z-15889/17 FIGI OB S500’ function [y, stałe] = Idfb80_32 (x, State) % wstępne fazowanie m = (32+1)/2;temp - u.5*conj (x).*exp( (2i*pi*((0:32-1)+0.5)*m/64));S510’ S520’ S530’ S542 S550 % nieparzysta symetria "temp = [temp conj (temp (32:-1:1))];% nieparzyste FFT y_knl = real (ifft (temp) .* exp(i*pi*(0:64-1)/64));% rozszerz dane;zmień znak przełączenia y_knl = -y_knl (64:-1:1): tmp = [y_knl -y_knl y_knl -y_knl y_knl]’;% okno syntezy win_ana = ldfb80_win;win_syn = win_ana(end:-1:1);win_syn = (win_syn(1:2:end)+wiirsyn(2:2:end))/2;zastosuj okno tmp = tmp.*win_sys;S560’ S570’ _% aktualizuj bufor State (320-32+(1:32)) State = state + tmp;% pozyskaj wyjście = 0;S580’ y — state(1:32);zmień bufor State (1:320-64) = State (32+1:320);FIG 11 Porównanie: Okno zespolonego modulowanego banku filtrów o małym opóźnieniu (CMLDFB) vs okno sinusowe okno CMLDFB okno sinusowe co ro CD 132 IN Ul oo OO CD ro o \i σι CD o oo FIG 12 Porównanie: Okno zespolonego modulowanego banku filtrów o małym opóźnieniu (CMLDFB) vs oryginalny prototypowy filtr SBR QMF ro o ro LO 133 IN I Ul LO "O ro o \i σι LO o NI oo FIG 13 Wielkość Porównanie: Kształt okna CLDFB vs oryginalny prototypowy QMF 32 /64 96 128 750 760 256 288 320 352 384 próbki ro I— 1 ro kO 134 Rdzeń modulacji 760 770 750 l\i I Ul OO OO kO "O ro o \i σ kO o oo 135 EP 2 076 901 B1 22/29 Z-15889/17 FIG 14A FIG 14B 136 EP 2 076 901 B1 23/29 Z-15889/17 FIG15A Odpowiedź częstotliwościowa 800 [χ π rad / i próbki i] Częstotliwość znormalizowana Omega/pi 137 EP 2 076 901 B1 24/29 Z-15889/17 FIG15B Odpowiedź częstotliwościowa Częstotliwość znormalizowana Omega/pi [χ π rad / próbki ] 138 EP 2 076 901 B1 25/29 Z-15889/17 Αί Φ JD "Ο IN (NI Φ C Φ 'c "Ο α. ο (D (_) (D C Αί Ο c Ν "Ο i_ Ν Φ ΤΤ Αί C D Φ C (D C ο CL CD CD ο £ ι Ο CO I Ο |Ν» I 9Ρ Omega/pi 139 EP 2 076 901 B1 26/29 Z-15889/17 Omega/pi Omega/pi ZT/688ST-Z 6Z/ZZ Ta T06 9Z0 Z d3 0t7[ 141 EP 2 076 901 B1 Z-15889/17 28/29 142 EP 2 076 901 B1 29/29 Z-15889/17 oryginalny sygnał czasu- (kastaniety si02)
1,710 paragraphs in 3 sections, as filed
Technical Field [0001] Embodiments of the present invention relate to an apparatus and method for generating audio subband values, apparatus and method for generating audio samples in the time domain and systems comprising any of the aforementioned devices that may, for example, be implemented in the field of modern coding audio, audio decoding or other audio-related applications.
[0002] Contemporary digital audio processing is usually based on coding schemes that allow for a significant reduction in bit rate, bandwidth, and storage space compared to direct transmission or storage of corresponding audio data. This is achieved by encoding the audio data at the sender's side and decoding the coded data at the receiver side before, e.g., providing the decoded audio data to the listener or for further signal processing.
[0003] Such digital audio processing circuits can be implemented in a wide range of parameters, usually affecting, on the one hand, the quality of data transmitted or otherwise processed, and on the other hand, computational efficiency, bandwidth and other performance related parameters. Very often, higher quality requires higher bit rates, greater computational complexity, and higher demand for storing the appropriate encoded audio data. Hence, depending on the intended application, factors such as acceptable bit rates, acceptable computational complexity and acceptable amount of data must be balanced by the desired and achievable quality.
[0004] Another parameter, which is particularly important in real-time applications, such as bi-directional or unidirectional communication, the delay imposed by different coding schemes may also play an important role. As a result, the delay imposed by audio encoding and decoding is another limitation in terms of the aforementioned parameters while balancing the needs and costs of different coding schemes, with a specific field of application in mind. As such, digital audio systems can be used in a wide variety of applications, ranging from extremely low quality transmissions to highest quality transmissions, various parameters and different limitations are often imposed on the audio systems concerned. In some applications, a lower delay may, for example,
[0005] However, in many cases, it may be necessary to compromise on various parameters such as bit rate, computational complexity, memory requirements, quality and latency.
[0006] "Enhanced MPEG-4 Low Delay AAC - Low Bitrate High Quality
Communication ", AES Convention Paper 6998, May 5, 2007 discloses an improvement for AAC Low Delay, which reduces bit rate requirements by 25-33%. This was achieved by using a delay optimized version of the Spectral Band Replication tool and by using a dedicated low-delay filter bank having the same cosine modulation functions as traditional MDCT.
[0007] EP 1 199 711 A1 discloses encoding an audio signal using bandwidth extension. The broadband and narrowband acoustic source signals are coded in such a way that the perceived sound quality of the respective reconstructed signals is improved. The improvement estimation unit perceptually improves the reconstructed acoustic source by using the spectrum of improvement. The asymmetric function of the window is positioned in the entire respective frame and extends over at least part of at least the previous frame.
[0008] "The Use Of Asymmetric Windows For Reducing The Time Delay In Real-Time Spectral Analysis", D. Florencio, ICRSP-91, volume 5, April 14, 1991 discloses the idea of asymmetric windowing as a way of reducing the time delay in spectral analysis. In particular, the use of LP speech coding, in particular CELP and LD-CELP, has been discussed.
Summary [0009] An embodiment of the apparatus for generating values of audio sub-bands with complex values is defined in claim 1. The embodiment of the device for generating audio samples with real-time values in the time domain is defined in claim 2.
[0010] Suitable methods are defined in claims 3 and 4.
Brief description of the drawings [0011] Embodiments of the present invention are described below with reference to the accompanying drawings.
Fig. 1 is a block diagram of an embodiment of the apparatus for generating audio subband values
Fig. 2a is a block diagram of an embodiment of the apparatus for generating time-domain audio samples;
Fig. 2b shows a functional principle according to an embodiment of the present invention in the form of a device for generating time-domain samples;
Fig. 3 shows the concept of interpolating window coefficients according to an embodiment of the present invention;
Fig. 4 shows the interpolation of window coefficients in the case of a sine window function;
Fig. 5 is a block diagram of an embodiment of the present invention comprising an SBR decoder and an SBR encoder;
Fig. 6 shows the source of the SBR system delay;
Fig. 7a is a flow chart of an embodiment of a method for generating audio subband values;
Fig. 7b illustrates a step of an embodiment of the method shown in Fig. 7a; Fig. 7c is a flow diagram of an example method for generating audio subband values;
Fig. 8a is a flow diagram of an example of a method for generating time domain samples;
Fig. 8b is a flow diagram of an example method for generating audio samples in the time domain;
Fig. 8c is a flowchart of a further embodiment of a method for generating time-domain samples;
Fig. 8d is a flow chart of another example of a method for generating time domain samples;
Fig. 9a illustrates a potential embodiment of an embodiment of a method for generating audio subband values;
Fig. 9b illustrates a potential implementation of an embodiment of a method for generating audio subband values;
Fig. 10a illustrates a potential implementation of an embodiment of a method for generating samples in the time domain;
Fig. 10b illustrates another potential implementation of an embodiment of a method for generating samples in the time domain;
Fig. 11 shows a comparison of a synthesis window function according to an embodiment of the present invention and a sine window function;
Fig. 12 shows a comparison of synthesis window functions according to an embodiment of the present invention and the function of a QMF SBR prototype filter;
Fig. 13 shows different delays caused by the window function and the prototype filter function shown in Fig. 12;
Fig. 14 is a table illustrating different contributions to the delay of the conventional AAC-LD + SBR codec and the AAC-ELD codec comprising an embodiment of the present invention;
Fig. 14b shows a further table including details of the delay of the various components of the various codecs;
Fig. 15a shows a comparison of a frequency response of a device based on a window function according to an embodiment of the present invention and an apparatus based on a sine window function;
Fig. 15b shows an enlargement of the frequency response shown in Fig.
15a;
Fig. 16a shows a comparison of the frequency response of 4 different window functions;
Fig. 16b shows an enlargement of the frequency responses shown in
Fig. 16a;
Fig. 17 shows a comparison of the frequency response of two different window functions, one asymmetric window function and one window function being a function of a symmetrical window; and
Fig. 18 schematically shows a general temporal masking property of a human ear;
Fig. 19 shows a comparison of an original audio time signal, a time signal generated based on the HEAAC codec and a time signal based on a codec comprising an embodiment of the present invention.
Detailed description of embodiments [0012] Figs. 1 to 19 are block diagrams and further graphs describing functional properties and features of various embodiments of devices and methods for generating audio subbands, devices and methods for generating time-domain samples and systems comprising at least one of the devices or methods mentioned above. However, before describing the first embodiment of the present invention in more detail, it should be noted that embodiments of the present invention may be implemented in hardware and software. Hence, the implementations described in the field of block diagrams of implementing the hardware data of the embodiments may also be treated as action networks of a corresponding embodiment of a corresponding method. Also,
[0013] The following describes the implementations of filter banks that can be implemented as analysis filter banks or synthesis filter banks. The analysis filterbank is a device for generating audio subband values in the audio subband channels based on (input) audio samples in the time domain being in a sequence of time extending from the previous sample to the subsequent sample. In other words, the term "analysis filter bank" can be used simultaneously as a synonym for an embodiment of the present invention in the form of an apparatus for generating audio subband values. Accordingly, the synthesis filter bank is a filter bank for generating audio samples in the time domain from the values of the audio subbands in the audio subband channels. In other words,
[0014] Both the analysis filter bank and the synthesis filter bank, which are also referred to in total as filter banks, can, for example, be implemented as modulated filter banks. Modulated filter banks, examples of which will be illustrated in more detail below, are based on oscillations at frequencies that are based on or derived from the center frequencies of the respective subbands in the frequency domain. The term "modulated" refers in this context to the fact that said oscillations are used in the context of a window function or a prototype filter function, depending on the specific implementation of such a modulated filter bank. Banks of modulated filters, as a rule, can be based on real-valued oscillations, such as harmonic oscillations (sine oscillations or cosine oscillations) or on appropriate oscillations with complex values (exponentially complex oscillations). Accordingly, modulated filter banks are referred to as real modulated filter banks, respectively, or filter filter filters with complex filter modulated filterbanks.
[0015] In the following description, embodiments of the present invention will be described in more detail in the form of modular banks with low delay modulation filters and real modulated low latency filter banks and respective program methods and implementations. One of the main applications of such low-delay modulated filter banks is the integration into the low latency spectral band replication (SBR), which is currently based on the use of a complex QMF filter bank with a symmetric prototype filter (QMF = mirror filter) quadrature Mirror Filter,) [0016] As will be understood in the course of this description,
[0017] Said improved balance, in particular between delay and reconstruction quality, is based on the approach of using so-called zero delay techniques to extend the filter impulse response of respective filter banks without introducing additional delay. A lower delay for a predetermined level of quality, a better quality at a predetermined level of delay or a simultaneous improvement in both delay and quality can be obtained by using an analysis filter bank and a synthesis filter bank according to an embodiment of the present invention.
[0018] Embodiments of the present invention are based on the finding that these improvements can be obtained by using a new window function for any of the two filter banks described earlier. In other words, the quality and delay can be improved for the analysis filterbank by using an analysis window function containing a window factor sequence that includes a first group comprising the first subsequent portion of the window coefficient sequence and a second window factor group comprising the second sequential portion of the window factor sequence. The first part and the second part contain all window coefficients of the window function. In addition, the first part contains fewer window coefficients than the second part, but the value of the total energy of the window coefficients in the first part is higher than the total energy value of the window coefficients of the second part. The first group of window coefficients is used for windowing the later time domain samples, and the second group of window coefficients is used for windowing the earlier time domain samples. This form of window function offers the possibility of processing time domain samples with window coefficients having higher energy values earlier. This is the result of the described distribution of window coefficients into two parts and their applications to the sequence of audio samples in the time domain. As a result of,
[0019] Accordingly, in the case of an embodiment of the present invention in the form of an apparatus for generating audio samples in the time domain and a corresponding method, the synthesis windowing module uses a synthesis window function that comprises a sequence of window coefficients aligned in the first (next) part and (next) the second part. Also, in the case of the synthesis window function, the total energy value of the window coefficient in the first part is higher than the energy value of the total window coefficient of the second part, the first portion comprising fewer window coefficients than the second part. Due to the distribution of window coefficients between the two parts and the fact that the synthesis windowing module uses the first part of window coefficients of the windowing module for windowing the later samples in the time domain,
[0020] A detailed description of the functions of the synthesis window and analysis window functions used in the framework of embodiments of the present invention will be set forth in more detail below. In many embodiments of the present invention, the sequence of window coefficients of the synthesis window function and / or the analysis window function comprises exactly the first group and the second group of window coefficients. In addition, each window coefficient coefficient window coefficient belongs to exactly one of the first group and the second group of window coefficients.
[0021] Each of the two groups contains exactly one part of the window coefficients arranged in sequence. In the present description, the part comprises a ranked set of window coefficients in accordance with the sequence of window coefficients. In the embodiments of the present invention, each of the two groups (first and second groups) contains exactly one part of the window coefficient sequence as described above. The relevant window coefficient groups do not contain any window coefficients that do not belong to exactly one part of the corresponding group. In other words, in many embodiments of the present invention, each of the first and second group of window coefficients comprises only the first part and the second part of the window coefficients and does not contain further window coefficients.
As part of this description, another part of the sequence of window coefficients is to be understood as a combined set of window coefficients in a mathematical sense, the set lacking window coefficients compared with the window coefficient sequence that would be within the range (e.g. index range) window coefficients of the relevant part. As a result, in many embodiments of the present invention, the sequence of window coefficients is divided exactly into two connected portions of window coefficients that form each of the groups of first or second window coefficients. In these cases, each window coefficient included in the first group of window coefficients is either placed in front of or behind each of the window coefficients of the second group of window coefficients relative to the entire sequence of window coefficients.
[0023] In other words, in many embodiments of the present invention, the sequence of window coefficients is divided exactly into two groups or parts without omitting any of the window coefficients. According to the sequence of window coefficients, which also represents their order, each of the two groups or parts includes all window coefficients up to (but only) or starting with (inclusive) the window coefficient of the window. For example, the first part or the first group may include window coefficients having indexes from 0 to 95 and from 96 to 639 for a window function containing 640 window coefficients (having indexes 0 to 639). In this case, the window threshold would be that corresponding to index 96. Naturally, other examples are also possible (e.g., 0 to 543 and 544 to 639).
The detailed illustrative embodiment of the analysis filter bank described below provides a filter length covering 10 blocks of input samples simultaneously introducing a system delay of only 2 blocks, which is a corresponding delay corresponding to the delay introduced by MDCT (modified discrete cosine transform) or MDST (modified discrete sine transformation). One of the differences results from the fact that for a longer length of the filter covering 10 blocks of input samples compared to the MDCT or MDST implementation, the overlap is increased from 1 block in the case of MDCT and MDST to the 9 block tab. However, further realizations covering a different number of blocks of input samples, which are also referred to, may also be realized, as audio input samples. In addition, other trade-offs may be considered and implemented.
[0025] Fig. 1 is a block diagram of an analysis filterbank 100 as an embodiment of an apparatus for generating audio subband values in audio subband channels. The analysis filter bank 100 includes an analysis windowing module 110 for windowing a frame of 120 input audio samples in the time domain. The frame 120 includes T blocks 130-1, 130-T, blocks (input) audio samples in the time domain, wherein T is a positive integer and is equal to 10 for the embodiment shown in Fig. 1. However, the frame 120 may also include different number of blocks 130.
Both the frame 120 and each of the blocks 130 comprise input audio samples in the time domain in a time sequence extending from the previous sample to a later sample according to the time line, as indicated by the arrow 140 in Fig. 1. In other words, in the illustration shown in Fig. 1, the farther to the right is a time-domain audio sample, which in this case is also an audio time-domain input sample, the later a corresponding time-domain audio sample relative to the sequence of the audio sample in the time domain.
The analysis windowing module 110 generates windowed time-domain samples based on the sequence of time-domain audio samples that are provided in a frame of 150 windowed samples. According to the frame 120 input audio samples in the time domain, also the frame of the windowed samples 150 contains T blocks of windowed samples 160-1, 160-T. In preferred embodiments of the present invention, each of the sample window blocks 160 comprises the same number of windowed samples as the number of input audio samples in the time domain of each block of audio input samples in the time domain. Hence, when each of the blocks 130 includes N input audio samples in the time domain, frame 120 and frame 150, each contain T · N samples. In this case, N is a positive integer that can, for example, be 32 or 64.
The analysis windshield module 110 is connected to the calculator 170 for calculating the values of the audio subbands based on the windowed samples provided by the analysis windower 110. The values of the audio subbands are provided by the calculator 170 as block 180 of the values of the audio subbands, each of the values of the audio subbands corresponding to one channel of the audio subband. In a preferred embodiment, also the audio subband value set 180 comprises N subband values.
[0029] Each of the audio subband channels corresponds to a characteristic center frequency. The center frequencies of the various audio subband channels may, for example, be evenly spaced or evenly spaced relative to the frequency bandwidth of respective audio signals as described for the time domain audio input inputs provided to the analysis filter bank 100.
[0030] The analysis windshield module 110 is adapted to windowing the input audio samples in the time domain of the frame 120 based on the analysis window function including a window coefficient sequence for obtaining windowed frame samples 150. The analysis window 110 is adapted to windshield the frame of the audio samples 120 in the field. time by multiplying the value of audio samples in the time domain by window coefficients of the analysis window function. In other words, windowing comprises multiplication depending on the element of the audio samples in the time domain by the corresponding window coefficient. Since both the frame of 120 audio samples in the time domain and the window coefficients contain the corresponding sequence,
[0031] In the embodiments of the present invention in the form of bank 100 of analysis filters, as shown in Fig. 1, the function of the analysis window, as well as the synthesis window function in the case of a synthesis filter bank, comprises only window coefficients with real values. In other words, each of the window coefficients assigned to the index of the window coefficient has a real value.
[0032] Window coefficients together form a corresponding window function, an example of which is shown in Fig. 1 as a function of the analysis window 190. As previously outlined, the sequence of window coefficients constituting the analysis window function 190 includes a first group 200 and a second window window coefficient group 210. The first group 200 comprises the first further and combined part of window coefficients of the window coefficient sequence, whereas the second group 210 comprises the second and the combined second part of the window coefficients. Together with the first part in the first group 200, they form the entire sequence of window coefficients of the function of the analysis window 190. In addition, each window coefficient coefficient window coefficient belongs to either the first part or the second part of the window coefficients, yes, that the entire function of the analysis window 190 is formed by the window coefficient of the first part and the second part. The first part of the window coefficients is therefore identical to the first group of 200 window coefficients, and the second part is identical to the second group of window coefficients 210, as shown by the respective arrows 200, 210 in Fig. 1.
[0033] The number of window coefficients in the first group 200 of the first portion of the window coefficients is smaller than the number of window coefficients in the second group of the second portion of the window coefficients. However, the value of the total energy of the window coefficients in the first group 200 is higher than the total energy of window coefficients in the second group 210. As described below, the value of the energy of the window coefficient set is based on the sum of squares of absolute values of the respective window coefficients.
In the embodiments of the present invention, the analysis window function 190, as well as the corresponding synthesis window function, is therefore asymmetric with respect to a sequence of window coefficients or a window coefficient index. Based on the set of index definitions of the window coefficients, in which the analysis window function 190 is defined, the analysis window function 190 is asymmetric, when for all n real numbers there is a further n0 real number so that the absolute value of the window coefficient corresponds to the index window coefficient (n0- n) window coefficient is not equal to the absolute value of the window coefficient corresponding to the index (n0 + n) of the window coefficient, when (n0-n) and (n0 + n) belong to the definition set.
[0035] In addition, as also shown schematically in Fig. 1, the function of the analysis window 190 includes character changes at which the product of two successive window coefficients is negative. More details and further features of the potential window functions according to embodiments of the present invention will be discussed in more detail below in the context of Figs. 11 to 19.
[0036] As previously stated, the window frame of samples 150 includes a similar block structure with individual blocks 160-1, 160-T as frame 120 of individual input samples in the time domain. Because the analysis windowing module 110 is adapted to windowing the input audio samples in the time domain by multiplying these values by window coefficients of the analysis window function 190, the frame 150 of windowed samples is also in the time domain. The calculator 170 calculates the values of the audio subbands, or, more precisely, the block 180 of audio subband values, using a frame of 150 windowed samples and realizes a transfer from the time domain to the frequency domain. The calculator 170 can thus be considered as a time-frequency converter that is capable of providing a block of 180 audio subbands values,
[0037] Each audio subband value of block 180 corresponds to one subband having a characteristic frequency. The number of audio subband values included in block 180 is sometimes also referred to as band number.
[0038] In many embodiments of the present invention, the number of audio subbands values in block 180 is identical to the number of audio time-domain input samples of each of frame blocks 130. In the case that the frame 150 of windowed samples has the same block-dependent structure. co-frame 120, so that each of the blocks 160 of the windowed samples also includes the same number of windowed samples as the block of these audio time input samples 130, the block 180 of the audio subbands naturally also contains the same number as the block 160.
[0039] The frame 120 may optionally be generated based on a block of fresh time input audio samples 220, by moving blocks 130-1, ..., 130 (T-1) one block in the opposite direction of arrow 140 indicating the direction of time. . In this way, the frame of the input audio samples in the time domain to be processed is generated by shifting (T-1) the last blocks of the immediately preceding frame 120 time-domain audio samples one block toward earlier audio samples in the time domain by adding a fresh block of 220 fresh time-domain audio samples as a new block 130-1 containing the last audio samples in the time domain of the current frame 120. In Fig. 1 this is also indicated by a series of dashed arrows indicating block displacement 130-1, .,
[0040] As a result of this block displacement 130 in the opposite direction of time, as shown by arrow 140, the current frame 120 to be processed comprises block 130- (T-1) of immediately preceding frame 120 as new block 130-T . Accordingly, blocks 130- (T-1), 130-2 of the current frame 120 to be processed are equal to block 130- (T-2), 130-1 directly to the preceding frame 120. Block 130-T immediately preceding frame 120 is removed.
[0041] As a result, each audio sample in the time domain of the fresh block 220 will be processed T times as part of T successive T-processes of successive audio time input frames of the audio samples. Thus, each audio input in time domain of fresh block 220 has a share not only in T of different frames 120, but also T of different frames of 150 windowed samples and T blocks 180 of audio subband values. As previously indicated, in a preferred embodiment of the present invention, the number of T blocks in frame 120 is equal to 10, so that each time-domain audio sample supplied to the analysis filter bank 100 has a share in the different audio subbands 180.
Initially, before the single frame 120 is processed by the analysis filter bank 100, the frame 120 may be initialized with a small absolute value (below a predetermined threshold), e.g. a value of 0. As explained in more detail below, the shape of the function 190 of the analysis window includes a center point or "center of mass" which usually corresponds or lies between the two indexes of the window coefficients of the first group 200.
[0043] As a result, the number of fresh blocks 220 to be introduced into the frame 120 is small before the frame 120 is filled at least until the frame 120 is occupied by non-zero (i.e., non-zero values) values that correspond to window coefficients with a significant share in terms of their energy value. Typically, the number of blocks to be inserted into the frame 120 before the "substantial" processing can begin is 2 to 4 blocks depending on the shape of the analysis window function 190. Hence, bank 100 of analysis filters is capable of delivering blocks 180 faster than a corresponding filter bank using, for example, a symmetrical window function. Since usually fresh blocks 220 are delivered to the bank of 100 analysis filters in their entirety, each of the fresh blocks corresponds to the time of registration or sampling, which is essentially given by the length of the block 220 (i.e., the number of input audio samples in the time domain included in block 220) and the sampling rate or frequency. Accordingly, the analysis window function 190 built into the embodiment of the present invention results in a reduced delay before the first and subsequent audio subbands 180 may be provided or derived by the filter bank 100.
[0044] As a further option, the device 100 may be capable of generating a signal or inputting a portion of information regarding a window analysis function 190 used in generating a frame 180 or relating to a synthesis window function to be used within a synthesis filter bank. In this way, the analysis window function 190 can be, for example, a time or index-reversed version of the synthesis window function to be used by the synthesis filter bank.
[0045] Fig. 2a shows a block diagram of an embodiment of apparatus 300 for generating time-domain audio samples based on a block of audio subbands values. As previously explained, an embodiment of the present invention in the form of an apparatus 300 for generating time-domain audio samples is often called a synthesis filter bank 300, because the device is capable of generating time-domain audio samples that can in principle be reproduced based on values audio subbands that contain spectral information related to the audio signal. Thus, the synthesis filter bank 300 is capable of synthesizing audio samples in the time domain based on the values of the audio subbands, which, for example, may be generated by an appropriate bank of 100 analysis filters.
[0046] Fig. 2a is a block diagram of a synthesis filter bank 300 comprising a calculator 310 to which a block of audio subbands (320) is allocated (in the frequency domain). The calculator 310 is able to calculate a frame 330 containing the sequence of intermediate time samples from the audio subbands of block 320. The 330 time domain intermediate frame 330 includes, in many embodiments of the present invention, a similar block structure as for example a windowed 150 frame. bank samples 100 of the analysis filters of Fig. 1.
In such cases, the frame 330 includes blocks 340-1, 340-T, intermediate blocks of time-domain samples.
[0048] The sequence of intermediate time-domain samples 330, as well as each block 340 intermediate time domain samples, contain a sequence in accordance with the course of time as indicated by the arrow 350 in Fig. 2a. As a result, the frame 330 includes an early intermediate time sample in block 340-T and the last intermediate time sample in block 340-1 that respectively represent the first and last time-domain intermediate samples for frame 330. Also, each of the blocks 340 contain a similar order. As a result, in the embodiments of the synthesis filter bank, the term "frame" and "sequence" can often be used synonymously.
[0049] The calculator 310 is connected to the synthesis windshielding module 360, to which frame 330 intermediate time domain samples are provided. The synthesis windowing module is adapted to windowing the intermediate sequence of samples in the time domain using the function 370 of the synthesis window schematically shown in Fig. 2a. At the output, the synthesis windshift module 360 provides a frame of 380 windowed intermediate time-domain samples that can also have a block-dependent structure, blocks 390-1, 390-T.
[0050] The frames 330 and 380 may respectively comprise T sides 340 and 390, wherein T is a positive integer. In a preferred embodiment of the present invention in the form of a synthesis filter bank 300, the number of T blocks is equal to 10. However, in other embodiments other number of blocks in one of the frames may also be included. More specifically, the number of T blocks may be greater than or equal to 3, or greater than or equal to 4, depending on the circumstances of the implementation and the previously explained compromises for embodiments of the present invention including a frame-based structure for both the filter bank 100 synthesis as well as a bank of 300 synthesis filters.
[0051] The synthesis windshield 360 module is connected to the output stage 400 of the overlap-add module, to which a frame 380 of windowed intermediate samples in the time domain is provided. The stage 400 of the insertion module with the overlap is capable of processing windowed intermediate time domain samples to obtain a block of 410 time domain samples. The block 410 (output) time-domain samples may then, for example, be delivered to further components for further processing, recording or transformation into auditory audio signals.
[0052] The calculator 310 for calculating the sequence of time-domain samples included in the frame 330 is able to convert data from the frequency domain into the time domain. Hence, the calculator 310 may include a frequency-time converter capable of generating a time-domain signal of the spectral representation contained in block 320 of the sub-bands of the audio. As explained in the context of calculator 170 of the analysis filter bank 100 shown in Fig. 1, each of the audio subbands of block 320 corresponds to an audio subband channel having a characteristic center frequency.
[0053] In contrast, the intermediate time domain samples included in the frame 330 represent, in principle, information in the time domain. The synthesis windowing module 360 is capable of and adapted to windowing the intermediate sequences of time domain samples contained in the frame 330 using the synthesis window function 370 as schematically shown in Fig. 2a. Synthesis window function 370 includes a sequence of window coefficients that also include a first group 420 and a second window coefficient group 430, as previously explained in the context of window function 190 with first group 200 and second window window coefficient 210.
[0054] The first group 420 of window coefficients of function 370 of the synthesis window includes a first sequential portion of the sequence of window coefficients. Similarly, the second group 430 of coefficients also comprises a second sequential portion of the window coefficient sequence, the first portion including fewer window coefficients than the second portion and wherein the energy value of the total window coefficients in the first portion is greater than the corresponding energy value of the total window coefficients of the second portion. The further features and properties of the synthesis window function 370 may be similar to the corresponding features and properties of the analysis window function 190, as schematically shown in Fig. 1. As a result, we refer here to the corresponding description within function 190 of the analysis window and a further description of the window function with reference to Figures 11 to 19,
For example, from the portions contained in the two groups 420, 430 of the window coefficients, each one typically creates a further and combined set of window coefficients, together comprising all window coefficients of window coefficients of the window function of window 370. In many embodiments of the present invention, the analysis window function 190, as shown in Fig. 1, and the synthesis window function 370, as shown in Fig. 2a, are based on each other. For example, the analysis window function 190 may be a time-reversed or inversely indexed version of the synthesis window function 370. However, other dependencies between the two window functions 190, 370 may also be possible. It may be advantageous to use the synthesis window function 370 as part of the synthesis windowing module 360, which is associated with the analysis window function 190,
[0056] As outlined in the context of Fig. 1, the synthesis filterbank 300 of Fig. 2a can optionally be adapted such that an incoming block 320 may include additional signals or additional pieces of information regarding a window function. For example, block 320 may include information regarding the analysis window function 190 used to generate block 320 or relating to function 370 of the synthesis window to be used by the synthesis windowing module 360. Hence, the filter bank 300 may be adapted to isolate relevant information and to provide it to the synthesis windowing module 360.
[0057] The outgoin stage of the tabbed addition module is capable of generating a block of 410 time-domain samples by processing windowed intermediate time-domain samples included in the frame 380. In various embodiments of the present invention, the 4000th stage of the add-on module with the tab may include memory for temporarily storing previously received frames of 380 windowed intermediate samples in the time domain. Depending on the details of the implementation, the output stage 400 of the add-on module with the overlap may, for example, comprise T of different recording items contained in the memory for storing the total number T of frames 380 windowed intermediate samples in the time domain. However, also a different number of recording positions can be included in the output stage 400 of the addition module with the tab, as required. In addition, in the various embodiments of the present invention, the output stage of the tab adding module may be capable of providing block 410 time-domain samples based on only one frame 380 intermediate time domain samples. Embodiments of different banks of 300 synthesis filters will be explained in more detail below.
[0058] Fig. 2b shows a functional principle according to an embodiment of the present invention in the form of a synthesis filter bank 300. The audio subbands 320 is first converted from the frequency domain to the time domain by the calculator 310, which is shown in Fig. 2b by arrow 440. A frame 320 of intermediate time-domain samples containing intermediate blocks 340-1, ..., 340-T has been created. time domain samples are then windowed by the synthesis windshift module 360 (not shown in Fig. 2b) by multiplying the intermediate sequences of time frame field samples 320 by a window sequence of window functions 370 of the synthesis window to obtain a frame 380 of windowed intermediate time domain samples. Box 380 again includes blocks 390-1, ..., 390-T, windowed intermediate time-domain samples,
an appropriate intermediate time sample in the time domain of the second block 390-2 of the frame 380-1 processed immediately before the frame 380 and written in the recording position at the 400th stage of the insertion module with the tab. As shown in Fig. 2b, subsequent respective windowed intermediate samples in the time domain of consecutive blocks 390 (e.g., block 390-3 of frame 380-2, block 390-4 of frame 380-3, block 390-5 of frame 380-4) are processed by the bank of 300 synthesis filters before they can be used. Frames 380-2, 380-3, 380-4 and optionally further frames 380 were processed by the bank of 300 filters in previous rounds. The frame 380-2 was processed immediately before the frame 380-1 and, accordingly, the frame 380-3 was processed immediately before the frame 380-2, etc. successive corresponding windowed intermediate samples in the time domain of consecutive blocks 390 (e.g., block 390-3 of frame 380-2, block 390-4 of frame 380-3, block 390-5 of frame 380-4) are processed by a bank of 300 synthesis filters, before can be used. Frames 380-2, 380-3, 380-4 and optionally further frames 380 were processed by the bank of 300 filters in previous rounds. The frame 380-2 was processed immediately before the frame 380-1 and, accordingly, the frame 380-3 was processed immediately before the frame 380-2, etc. successive corresponding windowed intermediate samples in the time domain of consecutive blocks 390 (e.g., block 390-3 of frame 380-2, block 390-4 of frame 380-3, block 390-5 of frame 380-4) are processed by a bank of 300 synthesis filters, before can be used. Frames 380-2, 380-3, 380-4 and optionally further frames 380 were processed by the bank of 300 filters in previous rounds. The frame 380-2 was processed immediately before the frame 380-1 and, accordingly, the frame 380-3 was processed immediately before the frame 380-2, etc. 380-4 and optionally further frames 380 have been processed by a bank of 300 filters in previous rounds. The frame 380-2 was processed immediately before the frame 380-1 and, accordingly, the frame 380-3 was processed immediately before the frame 380-2, etc. 380-4 and optionally further frames 380 were processed by a bank of 300 filters in previous rounds. The frame 380-2 was processed immediately before the frame 380-1 and, accordingly, the frame 380-3 was processed immediately before the frame 380-2, etc.
[0060] The outgoin stage 400 of the tab adding module used in the embodiment is able to sum for each block index 410 (output) of the time-domain T samples of different blocks 390-1, 390-T windowed intermediate time samples with T of different frames 380, 380-1, 380- (T-1). Thus, apart from the first T processed blocks, each of the (output) time-domain samples of block 410 is based on T of different audio subbands 320.
[0061] As with the embodiment of the present invention, bank 100 of the analysis filters described in Fig. 1, thanks to the synthesis window function form 370, the synthesis filterbank 300 offers the ability to quickly deliver block 410 (outbound) samples in the time domain. This is also the result of the window function function 370. Because the first group of window coefficients 420 corresponds to a larger energy value and includes fewer window coefficients than the second group 430, the synthesis windshift module 360 is capable of providing "significant" frames of 380 windowed samples when the 330 time domain intermediate time frame is filled such that the least window coefficients of the first group 420 have a share in box 380. The window coefficients of the second group 430 have a smaller share due to their lower energy value.
[0062] Hence, when the bank 300 of synthesis filters is initialized with 0, the provision of blocks 410 can, in principle, start as soon as several blocks of audio subband values are received by the synthesis filter bank 300. Hence, also a bank of 300 synthesis filters allows a significant reduction in the delay compared to a synthesis filter bank having, for example, a symmetrical function of the synthesis window.
[0063] As previously indicated, the calculators 170 and 310 of the examples shown in Figs. 1 and 2a may be implemented as real-value calculators generating or capable of processing audio subbands values with real values of blocks 180 and 320, respectively. In such cases, calculators may be, for example, implemented as real-value calculators based on harmonic oscillation functions, such as the sine function or the cosine function. In the exemplary embodiments, complex value calculators are implemented as calculators 170, 310. In these cases, the calculators may, for example, be implemented based on complex exponential functions or other harmonic functions with complex values. Oscillating frequencies with real or complex values usually depend on the audio subband value index, which is sometimes also referred to as a band index or a subband subband index of a given subband. In addition, the frequency may be identical or may depend on the center frequency of the respective subband. For example, the oscillation frequency may be multiplied by a constant factor, shifted relative to the center frequency of the respective subband, or may depend on a combination of both modifications.
[0064] The complex cost calculator 170, 310 may be constructed or implemented based on real value calculators. For example, in the case of a complex value calculator, efficient implementation, as a rule, can be applied to both the cosine- and sinus-modulated filter bank, representing the real and imaginary part of the composite component. This means that it is possible to implement both the cosine-modulated part and the sinus-modulated part based on, for example, the structure of the modified DCT-IV and DST-IV. In addition, further implementations may use the use of FFT (fast Fourier transformation) optionally implemented jointly for both,
Mathematical Description [0065] The following sections describe an example of an embodiment of an analysis filter bank and a synthesis filter bank with multiple block tabs for parts that do not cause further delays, as explained above, and one block into the future that causes the same delay as the structure MDCT / MDST (MDCT = Modified Discrete Cosine Transform, MDST = Modified Discrete Sine Transform). In other words, in the example below, the parameter T is equal to 10.
[0066] First, a description of the analysis filterbank modulated in a complex manner with a low delay will be described. As shown in Fig. 1, bank 100 of analysis filters includes the steps of window-winding analysis performed by the analysis windowing module 110, and the modulation of the analysis is performed by the calculator 170. The screening of the analysis is based on the equation from<sub>in</sub> = w (ΙΟΝ - 1 - n) · x<sub>in</sub> O <n <10 · N, (1) for where zi, n is a windowed sample (with actual values) corresponding to the index and block and the index n of the sample frame 150 shown in Fig. 1. The value xi, n is the input sample in the field time (actual values) corresponding to the same index and block as well as the n sample index. The function of the analysis window 190 is represented in equation (1) by its coefficient w (n) of the window with real values, where n is also the index of the window coefficient in the range indicated in equation (1). As already explained above, the parameter N is the number of samples in one block 220, 130, 160, 180.
[0067] From the arguments of the function in (10N-1-n) of the analysis window, it can be seen that the analysis window function represents an inverted version or a time-reversed version of the synthesis window function that is actually represented by window w (n) coefficients.
[0068] The modulation of the analysis performed by the calculator 170 in the embodiment shown in Fig. 1 is based on two equations
<img file="PL2076901T3_D0001.tif" />
<img file="PL2076901T3_D0002.tif" />
for the index of the spectral coefficient or index k of the band being an integer in the range
Ο <k <Ν. (4) [0069] The XReal values, i, ki Ximag, I, x represent the real part and imaginary part of the complex audio subband values corresponding to the index and block and k index of the spectral coefficient of block 180. The n0 parameter represents an index option that is equal to η<sub>0</sub> = -Ν / 2 + 0.5. (5) [0070] A suitable low modulus modular synthesis filter bank comprises the steps of transforming synthesis modulation, synthesis windowing and tab addition, as will be discussed below.
[0071] The synthesis modulation is based on the equation
<img file="PL2076901T3_D0003.tif" />
wherein x'i, n is an intermediate sample in the time domain of the frame 330 corresponding to the index n of the sample and the index and block. Again, the parameter N is an integer indicating the length of the block 320, 340, 390, 410, which is also called the transform block length, or, due to the structure dependent on the frame block 330, 380, as the previous block offset. Above, also further variables and parameters have been introduced, such as the index k of the spectral coefficient and the shift n0.
[0072] Synthetic winding implemented by the synthesis windshield 360 module in the embodiment shown in Fig. 2a is based on equation ζ '<sub>Α</sub>"= Κ (η) · x '<sub>and(</sub>"Ο <η <10 · Ν for (7) wherein z'i, n is the value of the windowed intermediate sample in the time domain corresponding to the index n of the sample and the index and block of the frame 380.
[0073] The addition transformation tag with the tab is based on the equation
<img file="PL2076901T3_D0004.tif" />
(8) for
0 £ η <Ν whereby outi, n represents the (output) sample in the time domain corresponding to the index n of the sample and the index and block. Equation (8) therefore illustrates the operation of adding a tabbed 400 stage output module with the overlap, as shown in the bottom part of Fig. 2b.
For comparison, for example, equations (2) and (6), for the cosine part, disclose that the proportion of cosine in the modulation analysis and in the synthesis modulation shows a comparable structure when considered for MDCT. Although the design method, in principle, allows the expansion of MDCT in both directions regarding time, here only the extension E (= T-2) of blocks is used in the past, with each of the T blocks containing N samples. The factor Xi, k of the frequency band k and the block and inside of the N-channel or N-band analysis filter bank can be summarized using
X \<sub>ik</sub> ^ = -2 <sup>V</sup>and(<sup>n</sup>) · <sup>Χ</sup>(<sup>Π</sup>) ' <sup>WHAT</sup>
<img file="PL2076901T3_D0005.tif" />
(9) for the index k of the spectral coefficient specified in equation (4). In this case, again n is the sample index, and wa is the function of the analysis window.
In order to ensure completeness, the mathematical description of the filter bank modulated in a complex manner with a low delay may be given in the same summary form as equation (9) by replacing the cosine function with an exponential function with complex values. More specifically, in the definitions and variables listed above, equations (1), (2), (3) and (5) can be summarized and expanded according to
<img file="PL2076901T3_D0006.tif" />
(10) whereas in contrast to equations (2) and (3), the expansion of 8 blocks into the past has been replaced by the variable E (= 8).
[0076] The steps of modulating synthetic synthesis and windowing, described for the complex case in equations (6) and (7), can be summarized in the case of a synthesis filter bank with real values. A frame of 380 windowed intermediate samples in the time domain, which is also called a demodulated vector, is given by
<img file="PL2076901T3_D0007.tif" />
(11) where z'i, n is a windowed intermediate time domain sample corresponding to the index and block and the n sample index. The n sample index is again an integer in the range
<img file="PL2076901T3_D0008.tif" />
aw ws (n) is a synthesis window that is compatible with the wa (n) window of analysis in equation (9).
[0077] The step of transforming the addition with the tab is given by
χ.
<img file="PL2076901T3_D0009.tif" />
r = (E + i) (13) where x'i, n is a reconstructed signal, or rather a time sample of block 410, provided by the 400th stage of the add-on module with the overlap shown in Fig. 2a.
[0078] For a bank of 300 complex synthesis filters, equations (6) and (7) can be summarized and generalized with respect to the extension E (= 8) of blocks in the path according to
<img file="PL2076901T3_D0010.tif" />
(14)
<img file="PL2076901T3_D0011.tif" />
Equation (8) and also applies to a complex-valued case.
[0079] As the direct comparison of equation (14) with equation (7) shows, the function w (n) of the window of equation (7) is the same function of the synthesis window as ws (n) of equation (14). As previously outlined, a similar comparison of the equation (10) with the weight coefficient (n) of the analysis window function with equation (1) shows that the analysis window function is a time-reversed version of the synthesis window function in the case of equation (1).
[0080] Since both the analysis filter bank 100 as shown in Fig. 1 and the synthesis filterbank 300 as shown in Fig. 2a offer a significant improvement in terms of the tradeoff between the delay on the one hand and the quality of the audio processing on the other hand, 100, 300 filter banks are often called low delay filter banks. Their complex values version is sometimes called a complex and low delay filter bank, which shortens as a CLDFB (complex-low-delay filterbank).
[0081] As shown in the previous discussion of the mathematical background, the frame used for implementing the proposed low delay filter banks uses a structure of the MDCT or IMDCT type (IMDCT = reversed MDCT), known from the MPEG-4 standard, using an extended overlap. Additional tab areas can be bound in a way that depends on the block with the left as well as with the right side of the MDCT core. In this case, only the right-side extension (for the synthesis filter bank) is used, which works only on the basis of past samples and therefore does not cause any additional delay.
[0082] Study of equations (1), (2) and (14) showed that the processing is very similar to MDCT or IMDCT processing. Thanks to only a small modification containing the modified function of the analysis window and the function of the synthesis window, respectively, MDCT or IMDCT is extended to a bank of modulated filters that is capable of handling multiple tabs and is very flexible in terms of its delay. As, for example, equations (2) and (3) have shown, the complex version, in principle, is obtained by simply adding a sinus modulation to a given cosine modulation.
Interpolation [0083] As outlined in the context of Figures 1 and 2a, both the analysis windowing module 110 and the synthesis windup module 360 or the corresponding filter banks 100, 300 are adapted to windowing respective time-domain sample frames by multiplying each of the respective audio samples. in the time domain by an individual window coefficient. Each of the time domain samples is, in other words, multiplied by the (individual) window coefficient, as, for example, equations (1), (7), (9), (10), (11) and (14) have shown. As a result, the number of window coefficients of the respective window function is usually identical to the number of corresponding audio samples in the time domain.
[0084] However, in some circumstances, it may be beneficial to implement a window function with a larger second window coefficient compared to the actual window function with a lower first coefficient number that is actually used when windowing a corresponding frame or sequence of audio samples in the time domain. This may, for example, be advantageous in the case where the memory requirements of a given implementation may be more valuable than computing efficiency. Another situation in which downsampling of window coefficients can be useful is the case of the so-called dual band approach, which is, for example, used in SBR (Spectral Band Replication) systems. The concept of SBR will be explained in more detail in the context of Figs. 5 and 6.
In this case, the analysis windower module 110 or the synthesis windower module 360 can additionally be adapted such that a suitable window function used for windowing the time domain audio samples provided to the respective windshift module 110, 360 is obtained by interpolating the coefficients windows of a larger window function with a softer second number of window coefficients.
[0086] Interpolation can, for example, be implemented by linear interpolation, polynomial interpolation or a spline curve. For example, in the case of linear interpolation, but also in the case of polynomial interpolation and with a spline, the corresponding windowing module 100, 360 may then be able to interpolate window coefficients of the window function used for windowing based on two successive window coefficients of a larger window function according to the sequence of coefficients windows of a larger window function for obtaining one window window function coefficient.
[0087] In particular, in the case of an equal number of audio samples in the time domain and window coefficients, the implementation of the interpolation as previously described leads to a significant improvement in the audio quality. For example, in the case of an even number of N · T time-domain audio samples in one of the frames 120, 330, not using interpolation, for example, linear interpolation will result in significant aliasing effects while further processing of corresponding audio samples in the time domain.
[0088] Fig. 3 shows an example of linear interpolation based on a window function (function of an analysis window or synthesis window function) to be used in the context of frames containing N · T / 2 audio samples in the time domain. Due to memory bounds or other implementation details, window coefficients of the window function itself are not stored in memory, but larger window functions containing N · T window coefficients are stored at the time of the corresponding memory or are otherwise available. Fig. 3 shows in the upper graph respective coefficients c (n) of the window as a function of indices n of window coefficients in the range between 0 and N · T-1.
[0089] Based on the linear interpolation of two successive window coefficients of a window function having a greater number of window coefficients, as shown in the upper graph of Fig. 3, the interpolated window function is calculated based on the ci [n] = j (c [2n] + equation c [2n + l]) <sub>d | g</sub>0 <η <W · Γ / 2. <sub>(15)</sub> [0090] The number of interpolated co-ordinates ci (n) of the window function window to be applied to a frame having N · T / 2 audio samples in the time domain comprises half the number of window coefficients.
[0091] To illustrate this additionally, in Fig. 3, the coefficients 450-0, ..., 450-7 of the window are shown in the upper part of Fig. 3, corresponding to coefficients c (0), ..., c (7) of the window . Based on these window coefficients and subsequent window window function coefficients, the use of equation (15) leads to the coefficients ci (n) of the interpolated window function window shown in the bottom part of Fig. 3. For example, based on the coefficients 450-2 and 450- 3 windows, the window coefficient 460-1 is generated based on equation (15) as shown by arrows 470 in Fig. 3. Accordingly, the window coefficient 460-2 of the interpolated window function is calculated based on the coefficients 450-4, 450 5 windows of the window function shown in the upper part of Fig. 3. Fig. 3 shows the generation of successive window coefficients ci (n).
[0092] To illustrate the aliasing cancellation that can be obtained by the interpolated decrease in sampling of the window function, Fig. 4 shows the interpolation of window coefficients for a sine window function that may, for example, be used in MDCT. For the sake of simplicity, the left half of the window function and the right half of the window function are drawn on each other. Fig. 4 shows a simplified version of a sine window containing only 2 · 4 window coefficients or points for an MDCT with a length of 8 samples.
[0093] Fig. 4 shows the four coefficients 480-1, 480-2, 480-3 and 480-4 of the window of the first half of the sine window and the four coefficients 490-1, 490-2, 490-3 and 390-4 of the second half window sine window. Window coefficients 490-1, ..., 490-4 correspond to coefficient indices 5, ..., 8 of the window. Window coefficients 490-1, ..., 490-4 correspond to the second half of the window function length, so that N '= 4 should be added to the indexes to obtain real indices.
[0094] To reduce or even obtain the cancellation of the aliasing effects, as explained earlier, the window coefficient should satisfy the condition v (n) · (Wl - n) = w (AZ '+ n) · w (2N' ~ 1 - η ) as much as possible. The better the dependency (16) is satisfied, the better the aliasing suppression or aliasing cancellation.
[0095] Assuming a situation in which a new window function having a half of the window coefficients for the left half of the window function is to be determined, the following problem arises. Because the window function has an even number of window coefficients (even number of reduced sampling) without using the interpolation scheme sketched in Fig. 3, the 480-1 and 480-3 or 480-2 and 480-4 window coefficients correspond to only one aliasing value the original window function or the original filter.
[0096] This leads to an unbalanced proportion of spectral energy and leads to an asymmetrical distribution of the center point (center of mass) of the corresponding window function. Based on the interpolation equation (15) for the window w (n) coefficient of Fig. 4, the interpolated I1 and I2 values satisfy the (16) aliasing dependence much better and therefore lead to a significant improvement in the quality of the audio data processed.
However, the use of an even more sophisticated interpolation scheme, e.g. a spline curve or other similar interpolation scheme, may even lead to window coefficients that more or less meet the relationship (16). Linear interpolation is in most cases sufficient and enables fast and efficient implementation.
[0098] The situation for a typical SBR system using a SBR-QMF filterbank (QMF = Quadrature Mirror Filter), linear interpolation or another interpolation scheme is not required for implementation, because the QBR prototype SBR filter contains an odd number the prototype filter coefficients. This means that the prototype SBR QMF filter contains a maximum value against which the reduced sampling can be performed, so that the symmetry of the SBR QMF prototype filter remains intact.
[0099] In Figs. 5 and 6, the potential use of the embodiments of the present invention will be described in the form of both an analysis filter bank and a synthesis filter bank. One important area of implementation is the SBR system or the SBR tool (SBR = Spectral Band Replication).
[0100] However, further applications of the embodiments according to the present invention may originate from other areas in which there is a need for a spectral modification (e.g., gain or correction modification), such as spatial audio object encoding, low delay stereo parametric coding, spatial coding / low delay surround, frame loss masking, echo cancellation or other suitable applications.
The basic idea underlying SBR is that there is usually a strong correlation between the properties of the high frequency range of the signal, which will be referred to as a so-called highband signal and low frequency band characteristics, referred to below as lower band or lowband signals, same signal . In this way, a good approximation of the representation of the original input highband signal can be obtained by transposing from the lower band to the upper band.
[0102] In addition to transposition, the upper-band reconstruction comprises shaping the spectral envelope that includes adjusting the gains. This operation is usually controlled by transmitting the highband spectral envelope of the original input signal. Another indication information sent from the encoder controls subsequent synthesis modules, such as reverse filtering, adding noise and sine to assist processing of the audio material when the transposition itself may not be sufficient. The corresponding parameters include "top noise band" parameters for adding noise and the "upper tonality band" parameter for adding a sine. This indication information is usually referred to as SBR data.
[0103] The SBR method may be combined with a conventional waveform or codec by means of an encoder side processing and post-coder final processing. SBR encodes parts of the high frequencies of the audio signal at a very low cost while the audio codec is used to encode parts of low signal frequencies.
[0104] On the coder side, the original input signal is evaluated, the upper band spectral envelope and its properties in relation to the lower band are coded, and the resulting SBR data is multiplexed with the bit stream from the bottom band codec. On the decoder side, the SBR data is first demultiplexed. The decoding operation is generally divided into stages. First, the core decoder generates a low bandwidth, and then the SBR decoder acts as a final processor using the decoded SBR data to drive the spectral band duplication operation. A full-band output signal is then obtained.
[0105] In order to obtain the highest possible coding efficiency and to maintain low computational complexity, improved SBR codecs are often implemented as so-called dual band systems. Dual range means that the limited bandwidth codec operates at half the external audio sampling rate. In contrast, part of SBR is processed at full sampling frequency.
[0106] Fig. 5 shows a schematic block diagram of a SBR system 500. The SBR system 500 includes, for example, the 510 AAC-LD encoder (AAC-LD = advanced audio codec low-delay) and the encoder 520 SBR, to which parallel audio data for processing is provided. The SBR encoder 520 includes a bank 530 of analysis filters, which is shown in Fig. 5 as a QMF analysis filter bank. The analysis filterbank 530 is capable of providing audio subband values to the respective subbands based on the audio signals supplied to the SBR 500 system. These values of the audio subbands are then provided to the SBR parameter acquisition module 540, which generates the SBR data as previously described, e.g. including the spectral envelope for the upper band, the upper band noise parameter, and the upper band tonality parameter.
[0107] The AAC-LD encoder 510 is shown in Fig. 5 as a two-range encoder. In other words, the encoder 510 operates at a frequency equal to half the sampling rate compared to the sampling frequency of the audio data provided to the encoder 510. To permit this, the AAC-LD encoder 510 includes a sample stage 550, which optionally may include a low pass filter to avoid distortion caused by, for example, failure to comply with the Nyquist-Shannon theorem. The reduced sampling audio data output from the sample stage 550 is then delivered to the 560 encoder (analysis filter bank) in the form of an MDCT filterbank. The signals provided by the encoder 560 are then quantized and coded at the quantizing and coding stage 570.
In addition, SBR data provided as provided by the S40 acquisition module 540 are also encoded to obtain the bitstream, which will then be output by the AAC-LD coder 510. The quantization and coding stage 570 may, for example, quantize data according to the auditory characteristics of the human ear.
[0108] The bitstream is then provided to the AAC-LD decoder 580, which is part of the decoder side to which the bit stream is delivered. The AAC-LD decoder includes a decoding and dequantization stage 590 that acquires SBR data from the bit stream and dequanized or re-quantized audio data in the frequency domain representing the low band. Bottom band data is then provided to a bank of 600 synthesis filters (reverse bank of MDCT filters). Stage 600 of inverted MDCT (MDCT<sup>-1</sup>) transforms the signals delivered to the inverted MDCT stage from the frequency domain into the time domain for providing a time signal. The time domain signal is then provided to the SBR decoder 610, which comprises the analysis filter bank 620, which is shown in Fig. 5 as the QMF analysis filterbank.
[0109] Bank 620 of the analysis filters performs spectral analysis of the time signal provided to bank 620 of the analysis filters representing the bottom band. This data is then delivered to the high frequency generator 630, which is also referred to as the HF generator. Based on SBR data provided by the AAC-LD encoder 580 and its decoding and dequantizing stage 590, the H30 generator 630 generates a topband based on the lower band signals provided by the bank 620 of the analysis filters. Both the lowband signal and the highband signal are then supplied to the synthesis filter bank 640, which converts the lowband and highband signals from the frequency domain to the time domain for providing the time domain audio output signal from the SBR system 500.
[0110] For completeness, it should be noted that, in many cases, the SBR 500 system, as shown in Fig. 5, is not implemented in this way. More specifically, the AAC-LD encoder 510 and the SBR encoder 520 typically are implemented on the encoder side, which is typically implemented separately from the decoder side comprising the AAC-LD decoder 580 and the SBR decoder 610. In other words, system 500 shown in Fig. 5 substantially represents a combination of two systems, namely an encoder comprising said encoders 510, 520 and a decoder comprising said decoders 580, 610.
[0111] Embodiments according to the present invention in the form of banks 100 analysis filters and banks 300 synthesis filters may, for example, be implemented in the system 500 shown in Fig. 5, as a replacement for the bank 530 of the analysis filters, the bank 620 filter banks and the bank 640 filters synthesis. In other words, the synthesis filter banks or analysis of the SBR components of the system 500 may, for example, be replaced by corresponding embodiments of the present invention. In addition, MDCT 560 and inverted MDCT 600 can also be replaced by low-latency analysis and synthesis filter banks, respectively. In this case, if all described replacements are implemented, the so-called improved low-latency AAC codec (codec = codec-decoder) will be implemented.
[0112] The improved AAC (AAC-ELD) with low latency aims to combine the low latency characteristics of AAC-LD (Advanced Audio Codec - Low-delay) with HE-AAC (high performance) encoding efficiency. advanced audio codec, High Efficiency Advanced Audio Codec) by using SBR with AAC-LD. The SBR decoder 610 operates in this situation as a final processor, which is provided after a core 580 decoder, including a complete analysis filterbank and a bank 640 of synthesis filters. Accordingly, the SBR decoder components 610 add a further decoding delay, as illustrated in Fig. 5 by the components 620, 630, 540.
[0113] In many embodiments of the 500 SBR, the low frequency parts or the low frequency band typically comprises from 0 kHz to typically 5-15 kHz and are encoded using a waveform encoder, termed the core codec. The core codec can be, for example, one of the MPEG audio codec family. In addition, the reconstruction of high frequency parts or the upper band is performed by transforming the lower band. The SBR combination with the core coder is in many cases implemented as a dual band system with the AAC encoder / decoder operating at half the SBR encoder / decoder sample rate.
[0114] Most control data is used for the representation of a spectral envelope that has variable time and frequency resolution to provide the best possible controllability of the SBR operation with the lowest bit rate imposed. Other control data are mainly intended to control the tonality relation to the upper band noise.
[0115] As shown in Fig. 5, the output from the base AAC decoder 580 is typically analyzed using a 32-channel bank QMF filter 620. Next, the HF generator module 630 reproduces the upper band by patching the QMF subbands from the existing lower band to the upper band. In addition, reverse filtering is performed for each subband, based on the control data acquired from the bit stream (SBR data). The envelope alignment modifier modifies the spectral envelope of the regenerated upper band and adds additional components such as noise, and sinusoids are added according to the control data in the bit stream. Since all operations are performed in the frequency domain (also shown as a QMF or subband area), the final stage of the decoder 610 is a QMF 640 synthesis for the preservation of the time domain signal. For example,
[0116] In addition, the delay of the core encoder 510 is doubled by operating at half the sampling rate in the dual band mode, which creates additional delay sources both in the encoder processing and the AAC-LD decoder in combination with the SBR. Below, such delay sources are examined and their associated delay is minimized.
[0117] Fig. 6 shows a simplified block diagram of a system 500 shown in Fig. 5. Fig. 6 focuses on delay sources in encoder / decoder processing using SBR and a low delay filter bank for coding. Comparing Fig. 6 of Fig. 5, MDCT 560 and inverted MDCT 600 were replaced by optimized delay modules, so-called MDCT 560 'with low latency (LD MDCT) and inverted MDCT 600' with low latency (LD MDCT). In addition, the 630 HF generator also has to be replaced by the module 630 'with an optimized delay.
[0118] In the system shown in Fig. 6, apart from MDCT 560 'low latency and inverted MDCT 600' with low latency, modified SBR framing and modified HF 630 'generator are used. To avoid delays due to different framing of the 560, 600 core coder / decoder and corresponding SBR modules, the SBR framing is adapted to fit the AAC-LD sample length of 480 or 512 samples. In addition, the variable time grid of the 630 HF generator, which implies 384 delay samples, is limited in the scope of extending the SBR data to the adjacent AC-LD frames. In this way, the only remaining sources of the SBR module delay are the 530, 620 and 640 filters.
[0119] According to the situation shown in Fig. 6, representing the partial implementation of the AAC-ELD codec, some delay optimization has already been implemented, including the use of a low delay filter bank in the AAC-LD core and removal of the previously mentioned SBR tab. For further delays, the remaining modules should be examined. Fig. 6 shows the delay sources in an encoder / decoder operation using SBR and low delay filter banks, referred to herein as MDCT and LDMDCT. Compared to Fig. 5, in Fig. 6, each rectangle represents the delay source, wherein the optimized delay modules are drawn shaded. Similar modules have not been optimized for low latency.
[0120] Fig. 7a illustrates a flowchart comprising a pseudo C- or C ++ -code to illustrate an embodiment of the present invention in the form of an analysis filter bank or the corresponding method of generating audio subbands in channels of audio subbands. To be more precise, Fig. 7a is a flowchart of an analysis filter bank with complex values for 32 bands.
[0121] As outlined above, the analysis filterbank is used to divide the time domain signal, e.g., outputted from the core coder, into N = 32 subband signals. The output from the filterbank, subband samples or values of the audio subbands, have in the case of a complex analysis filter bank complex values and are therefore oversampled with factor 2, in comparison with the real value filter bank. The filtering requires and includes the following steps, wherein the table x (n) contains exactly 320 time domain samples. The higher the sample index n in this table, the older the samples are.
[0122] After the execution of the embodiments of the method in step S100, first, the samples in table x (n) are shifted by 32 positions in step S110. The oldest 32 samples are removed and 32 new samples are stored in positions 31 to 0 in step S120. As shown in Fig. 7a, incoming time-domain audio samples are stored at positions corresponding to the decreasing index n in the range of 31 to 0. This leads to a time reversal of samples stored in the appropriate frame or vector so that the index of the window function is already inverted to obtain analysis window functions based on the (equally long) function of the synthesis window.
[0123] In step S130, window coefficients ci (j) are acquired by linear interpolation of coefficients c (j) based on equation (15). Interpolation is based on block size (block length or number of subband values) N = 64 values and based on a frame containing T = 10 blocks. Thus, indexes of window coefficients of an interpolated window function are in the range between 0 and 319 according to equation (15). The coefficients c (n) of the window are given in the table in annex 1 of the description. However, depending on the implementation details, to obtain window coefficients based on the values given in the tables in annexes 1 and 3, additional changes of the sign relative to window coefficients corresponding to indexes 128 to 255 and 384 to 511 (multiplication by factor (-1)) should be considered.
[0124] In these cases, the coefficients w (n) or c (n) of the window to be used can be obtained according to = <sup>IN</sup>tabi<sub>e</sub>In ' <sup>S</sup><<sup>n</sup>), (16a) with the function s (n) change of the sign according to s (n)
- 1 for 128 <n <
+ 1
k.
255 and
In the other case
<img file="PL2076901T3_D0012.tif" />
for n = 0 to 639, where wtable (n) are values given in tables in annexes. [0125] However, the window coefficients do not have to be used according to the table in annex 1 to obtain, for example, the delay reduction already described. To obtain this delay reduction, while maintaining the quality level of the audio data being processed, or to achieve a different compromise, the window coefficients c (n) for the n index of the window coefficient in the range between 0 and 639 may satisfy one of the dependency sets as given in one from annexes 2 to 4. In addition, it should be noted that also other coefficients c (n) of the window may be used in the embodiments of the present invention. Naturally, other window functions may also be implemented, containing a different number of window coefficients than 320 or 640,
[0126] The linear interpolation of S130 leads to a significant improvement in the quality and reduction or deletion of the effects of aliasing in the case of a window function comprising an even number of window coefficients. In addition, it should be noted that the complex unit is not like in equations (1), (2) and (16), but it is marked by<sup>A 1</sup> ·.
[0127] In step S140, samples of the table x (n) are then multiplied depending on the element by the coefficients ci (n) of the interpolated window.
[0128] In step S150, the windowed samples are summed according to the equation given in the flow diagram in Fig. 7a to create the 64-element array u (n). In step S160, 32, new subband samples or W (k, 1) audio subbands are calculated according to the matrix Mu operation, wherein the elements of the matrix M are given by
<img file="PL2076901T3_D0013.tif" />
where exp () means a complex exponential function, and as mentioned above, and is an imaginary unit. Before the activity network loop ends in step S170, each of the values of W (k, 1) (= W [k] [1]) subbands can be derived, which corresponds to the sample 1 subband in the subband with index k. In other words, each loop in The network of operations shown in Fig. 7a generates 32 subband values with complex values, each representing an output from one subbands of the filter bank.
[0129] Fig. 7b shows a step S150 of collapsing a frame of 150 windowed audio samples in a time domain comprising 10 sides 160-1, ..., 160-10 windowed samples from (n) audio in time domain to a vector in (n) by summing up the two blocks of the 150 frame each five times. Coiling or undo are made depending on the item, so that windowed audio samples in the time domain correspond to the same sample index within each of blocks 160-1, 160-3, 160-5, 160-7 and 160-9 are added to obtain the corresponding value in the first blocks 650-1 of the vector u (n). Accordingly, based on blocks 160-2, 160-4, 160-6, 160-8 and 160-10, corresponding elements of the vector u (n) in block 160-2 are generated in step S150.
[0130] A further embodiment of the present invention in the form of an analysis filter bank may be implemented as a 64-band complex filter bank with low delay. The processing of this complex low-latency filter bank as an analysis filter bank is basically similar to the analysis filter bank described in the context of Fig. 7a. Because of the similarities and essentially the same processing as described in the context of Fig. 7a, the differences between the described complex analysis filter bank for the 32 bands of Fig. 7a and the complex analysis filterbank for the 64 subbands will be outlined here.
[0131] In contrast to the 32-subband analysis filterbank as shown in Fig. 7a, the frame vector x (n) contains, in the case of a 64-band bank 640 analysis filters, elements having indexes 0 to 639. Thus, the step S110 is modified in such a way that the samples in table x (n) are shifted by 64 positions, the oldest 64 samples being removed. In step S120 instead of 32 new samples, 64 new samples are stored in positions 63 to 0. As shown in Fig. 7c, incoming time-domain audio samples are stored in positions corresponding to the decreasing index n in the range of 63 to 0. This leads to a time reversal samples stored in a suitable frame or vector such that a reversal of the window function index is provided to obtain the analysis window function based on the (equally long) function of the synthesis window.
[0132] Since the window c (n) used for windowing the frame vector elements x (n) usually contains 640 elements, it is possible to omit step S130 for linear interpolation of window coefficients to obtain interpolated windows ci (n).
[0133] Then, in step S140, the samples of the table x (n) are multiplied or windowed using a sequence of coefficients c (n) of the window, which are, again, based on the values in the table in annex 1. Where coefficients c ( n) windows are window coefficients of the synthesis window function, windowing or multiplication of the x (n) table by the window c (n) is carried out in accordance with the equation ζ (η) = χ (η) · c (n), <sub>(1θ)</sub> for an = 0, ..., 630. Again, to achieve the low latency properties of the window function, it is not necessary to implement the window function exactly according to the window coefficients based on the values given in the table in Annex 1. For many applications, the implementation in which window coefficients meet any set of dependencies as given in the tables in annexes 2 to 4, will be sufficient to obtain an acceptable compromise between quality and a significant reduction in delay. However, depending on the implementation details, in order to obtain window coefficients based on the values given in the tables in Annexes 1 and 3, additional changes of the sign relative to window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplication by factor (-1)) be considered in accordance with equations (16a) and (16b).
[0134] Step S150 of the flowchart shown in Fig. 7a is then replaced by summing the frame vector samples with (n) according to the equation
.... ' <sup>AT</sup>F) = Σ (<sup>η</sup> + J ' <sup>12θ</sup>) (19) to create a 128-element array of u (n).
[0135] Step S160 of Fig. 7a is then replaced by a step in which the 64 new subband samples are calculated according to the Mu Mu matrix operation, wherein the elements of the matrix, matrix M, are given by <sub>M</sub>(<sub>k</sub>, n) = 2 - e<sup>1</sup> ' <sup>+</sup> ° ^<sub>3</sub> <<sup>2</sup><sup>n</sup> - <sup>191</sup>>), {
O <k <64 O <n <128> (2θ) where exp () means an exponential complex function, and is, as explained, an imaginary unit.
[0136] Fig. 7c is a flowchart according to an example in the form of an analysis filter bank with real values for 32 subband channels. The embodiment, as shown in Fig. 7c, does not differ significantly from the embodiment shown in Fig. 7a. The main difference between the two embodiments is that step S160 calculating the new 32 values of complex audio subbands is replaced in the embodiment shown in Fig. 7c by step S162, in which 32 samples of real-valued audio subbands are calculated in accordance with the Mru operation. matrix, where the elements of the matrix Mr are given by
<img file="PL2076901T3_D0014.tif" />
[0137] As a result, each loop in the flow network produces 32 subband samples with real values, W (k, 1) corresponds to sample 1 of the audio subband of subband k.
[0138] The real-valued analysis filter bank may, for example, be used as part of the SBR low-power mode as shown in Fig. 5. The low power mode of the SBR tool differs from the high quality SBR tool mainly in that the banks are used filters with real values. This reduces the computational complexity and computational effort by factor 2, so that the number of operations per unit of time is substantially reduced by factor 2, because no imaginary part needs to be calculated.
[0139] The proposed new filter banks according to the present invention are fully compatible with the low power mode of SBR systems. Accordingly, with the filter banks according to the present invention, the SBRs can still operate either in normal mode or in high quality mode with combined filter banks and in low power mode with real value filter banks. Real-valued filter banks can, for example, be derived from combined filter banks by using only real values (shares with cosine modulation) and bypassing imaginary values (shares with sine modulation).
[0140] Fig. 8a is a flow chart according to an embodiment of the present invention in the form of a complex synthesis filter bank for 64 subband channels. As previously outlined, filtering of the syntax of subband signals processed by SBR is obtained using a 64-sub sample synthesis filter bank according to an embodiment of the present invention. At the output of the filterbank is a block of real-time value-domain samples as outlined in the context of Fig. 1. The operation is illustrated by the flow chart in Fig. 8a, which also illustrates an embodiment of the present invention in the form of a time-domain audio-generating method.
[0141] The synthesis filtration includes after the start (step S200) the following steps, wherein the table v contains 1,280 samples. In step S210, the samples in the table v are shifted by 128 positions, with the oldest 128 samples being removed. In step S220, 64 new values of the audio subbands of complex values are multiplied by the matrix N, where the elements N (k, n) of the matrix are given by
2V (k, η) = -L. exp | 64 I
128 and π · (k + 0.5) (2 η
<img file="PL2076901T3_D0015.tif" />
Ο <k <64 Ο <η <128 '(22) where exp () means an exponential complex function, and i is an imaginary unit. The actual part of the result of this operation is stored in the position 0-127 of the table v, as shown in Fig. 8a.
[0142] In step S230, the samples that are now in the time domain are obtained from the table v according to the equation given in Fig. 8a to create a 640-element array g (n). In step S240, the real-valued samples in the time domain of the array g are multiplied by the coefficient c (n) of the window to form the array w, the window coefficients of the preferred embodiment according to the present invention again being window coefficients based on the values given in the table in annex 1 .
[0143] However, as previously outlined, the window coefficients do not have to be based exactly on the values given in the annexe table. In other embodiments of the present invention, it is sufficient if the window coefficients satisfy one of the set of dependencies given in the appendixes 2 to 4 , to achieve the desired low delay property of the synthesis filter bank. In addition, as explained in the context of the analysis filterbank, other window coefficients can also be used as part of the synthesis filter bank. However, depending on the details of implementation, for obtaining window coefficients based on the values given in the tables in Annexes 1 and 3,
[0144] In step S250, 64 new output samples are calculated by summing samples from the table at (n) according to the last formula step given in the flow diagram of Fig. 8a before the loop of the activity network ends at step S260. In the flowchart shown in Fig. 8a, X [k] [1] (= X (k, 1)) corresponds to 1 audio subbands in the subband with index k. Each new loop shown in Fig. 8a outputs 64 audio samples with real values in the domain of time.
[0145] The implementation shown in Fig. 8a of the complex analysis filter bank for 64 bands does not require an add buffer with a tab containing several storage positions, as explained in the context of the embodiment shown in Fig. 2b. In this case, the addition buffer with the tab is "hidden" in the vig vectors, which is calculated based on the values stored in the vector v. The addition buffer with the tab is implemented within these vectors, with these indexes being greater than 128, such that values correspond to values from previous or previous blocks.
[0146] Fig. 8b is a flowchart of a synthesis filter bank with real values for 64 channels of audio subbands with real values. The synthesis filter bank with real values according to Fig. 8b can also be implemented in the case of implementing low power SBR, as an appropriate SBR filter bank.
[0147] The flow diagram of Fig. 8b differs from the flow diagram of Fig. 8a mainly in step S222, which replaces step S220 in Fig. 8a. In step S222, 64 new values of the real-valued audio subbands are multiplied by the matrix No., wherein the elements of the matrix No. (k, n) are given by
<img file="PL2076901T3_D0016.tif" />
the result of this operation is again stored in positions 0-127 of the table v.
[0148] In addition to these modifications, the flowchart shown in Fig. 8b for a synthesis filter bank with real values for the SBR low power mode does not differ from the flowchart shown in Fig. 8a of the synthesis filter bank of complex values for high quality SBR mode. .
[0149] Fig. 8c shows a flowchart in accordance with an embodiment of the present invention in the form of a composite synthesis filter bank, with reduced sampling and a corresponding method that may, for example, be implemented to implement high quality SBR. More specifically, the synthesis filter bank described in Fig. 8c relates to a composite synthesis filterbank, capable of processing audio subband values with complex values for 32 subband channels.
[0150] The synthesis filtration with reduced sampling of the SBR processing subband signals is obtained using the 32-channel synthesis filter bank shown in Fig. 8c. At the output of the filter bank is a block of real-time samples. The method is depicted in the flow chart of Fig. 8c. The synthesis filtration includes after the start (step S300) the following steps, wherein the table v contains 640 real-time value-domain samples.
[0151] In step S310, the samples in the table v are shifted by 64 positions, with the oldest 64 samples being removed. Then, in step S320, 32 new subband samples with complex values or complex subband audio subbands are multiplied by the matrix N, the elements of which are given by
<img file="PL2076901T3_D0017.tif" />
where exp () stands for an exponential complex function, and i is, again, an imaginary unit. The real part at the output of the operation is then stored in positions 063 of the array v.
[0152] In step S330, the samples are extracted from the vector v according to the equation given in the flow diagram in Fig. 8c to form the 320 element g. In step S340, the coefficients ci (n) of the windows of the interpolated window function are acquired by interpolation the linear coefficients c (n) according to equation (15), where the index n is again in the range between 0 and 319 (N = 64, T = 10 for equation (15)). As it was illustrated earlier, window coefficients c (n) are based on the values given in the Appendix 1 table. Additionally, to obtain the low latency properties, as it was already illustrated, window coefficients c (n) do not have to be exactly the numbers given in the annex table 1. It is sufficient if the coefficients c (n) of the window satisfy at least one of the set of dependencies given in appendixes 2 to 4. However, depending on the details of the implementation, in order to obtain window coefficients based on the values given in the annexes 1 and 3 tables, additional changes to the window ratios corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplication by factor (-1)) according to equations (16a) and (16b ). In addition, naturally also other window functions including other window coefficients c (n) may be used in the embodiments of the present invention.
In step S350, the samples of the array g are multiplied by the interpolated coefficients ci (n) of the window of the interpolated window function for obtaining windowed samples in (n) in the time domain.
[0154] Then, in step S360, 32, the new starting samples are calculated by summing the samples from the table at (n) according to the last step S360, before the final step S370 in the flow network of Fig. 8c.
[0155] As previously indicated, in the flowchart of Fig. 8c, X ([k] [l]) (= x (k, 1)) corresponds to the value of 1 audio subbands in the channel k of the audio subband. In addition, each new action network loop, as indicated in Fig. 8c, outputs 32 real-time sample outputs on the output.
[0156] Fig. 8d shows a flow diagram of an example according to the present invention in the form of a synthesis filter bank with real values and reduced sampling, which, for example, can be used in the case of a low power SBR filter bank. The example and network of operations shown in Fig. 8d differ from the flowchart shown in Fig. 8c of the composite synthesis filterbank and reduced sampling only in the scope of step S320 which is replaced in the flowchart shown in Fig. 8d via step S322.
[0157] In step S322, 32 new values of the audio subbands of real values or sample subbands are multiplied by the matrix No., wherein the elements of the matrix No. are given by
<img file="PL2076901T3_D0018.tif" />
the result of this operation is stored in position 0 to 64 of the table v.
[0158] Fig. 9a shows a further embodiment of an embodiment of the present invention in the form of a method corresponding to a complex analysis filter bank for 64 subbands. Fig. 9a shows the implementation of the MATLAB implementation which outputs the vector y and the "state" vector. The function defined in this script, shown in Fig. 9a, is called LDFB80 and to which the vector x is input as input, containing fresh audio samples and the "state" vector. The function name LDFB80 is an abbreviation for a low delay filter bank for 8 blocks extending into the past and 0 blocks extending into the future.
[0159] In the MATLAB programming language, the percent sign (%) means a comment that is not implemented but only serves to describe and illustrate the source code. In the following description, different segments of the source code will be explained in terms of their function.
[0160] In the S400 sequence of the code, the buffer that is represented by the "state" vector is updated such that the content of the "state" vector with indices 577 to 640 is replaced by the contents of the vector x containing fresh input audio samples in the time domain. In the S410 sequence of the code, window coefficients of the analysis window function that are stored in the LDFB80_win variable are converted into the win_ana vector.
[0161] In step S420, in which the last samples are assumed to be aligned to the right-hand buffer, actual windowing takes place. In block S420, the content of the state vector is multiplied depending on the element (. *) By the elements of the win_ana vector containing the function of the analysis window. The result of this multiplication is then saved in the x_win_orig vector.
[0162] In step S430, the content of the x_win_orig vector is transformed to form a 128 & lt; 5 & gt; array of elements called x_stack. In step S440, the change in the x_stack stack character is performed relative to the second and fourth columns of the x_stack matrix.
[0163] In step S450, the x_stack stack is folded or rolled back by summing the x_stack elements relative to the second index and simultaneously inverting the order of the elements and transposing the result before storing the result again for different x_stack.
[0164] In the S460 segment of the code, the time-domain transformation into the frequency domain is performed by computing the complex fast Fourier transform (FFT) of the element-multiply stack x_stack multiplied by the complex exponential function for which the argument is supplied (-i · π · n / 128), with indexes ranging from 0 to -127 and unit and imaginary.
[0165] In the S470 segment, the final twiddle is performed by defining the variable m = (64 + 1) / 2 and by calculating the block containing values of the audio subbands as the vector y according to the equation y (<sup>k</sup>) = 2 · temp (k) · exp (- 2i · · ((k - 1 + |) · ^)). <sub>(26)</sub>
The index k covers the range of integers from 1-64 in the embodiment shown in Fig. 9a. The vector y is then output as a vector or block containing the values of the 180 audio subbands of Fig. 1. The line over the second factoring equation (26) as well as the conj () function encodes the segment S417 in Fig. 9a refer to the complex complex number of the argument of the corresponding complex number.
[0166] In the final segment of the code S480, the state vector is shifted by 64 elements. The state vector in its offset form may then be provided to the LDFB80 function as input again in the next function loop.
[0167] Fig. 9b shows the MATLAB implementation according to an embodiment of the present invention in the form of a method relating to an analysis filter bank with complex values for 32 subbands. Accordingly, the defined function is called LDFB80_32 indicating that the implementation represents a low delay filter bank for 32 subbands based on the additional tab 8 blocks in the past and 0 blocks in the future.
[0168] The embodiment of Fig. 9b differs from the embodiment shown in Fig. 9a only in terms of several code sequences and will be outlined in the description below. The sequences S400, S430, S460, S470 and S480 of the code are replaced by the respective sequences S400 ', S430', S460 ', S470' and S480 'code mainly considering that the number of subbands, or the number of subband values output by the LDFB80_32 function is reduced by equal to 2. The step S400 'refers to the state of the vector updated in terms of 32 recent entries corresponding to indexes 289 to 320 with corresponding input audio samples 32 in the time domain of fresh block 220, as shown in Fig. 1.
[0169] However, the main difference between the embodiments shown in Figs. 9a and 9b appears in the sequence S410 of the code in Fig. 9a, which is replaced by the sequence code S412 in the embodiment shown in Fig. 9b. The code sequence for S412 in Fig. 9b comprises firstly copying 640 window coefficients comprising windows stored in the LDFB80_win vector into the local win_ana vector. Next, interpolation takes place according to equation (15), in which two successive window coefficients represented by vector elements, the win_ana vector, are added and divided by 2, and then stored back in the win_ana vector.
The next sequence code S420 is identical to the code sequence S420 shown in Fig. 9a, which realizes the actual multiplication depending on the element (. *) Windowing values, or elements, state state by elements of the win_ana vector including interpolated window coefficients of the interpolated window function. The result of this operation is the x_win_orig vector that is stored. However, the difference between the code sequence S420 of Fig. 9b and the corresponding code sequence S420 of Fig. 9a is that for Fig. 9b, not 640, but only 320 multiplication operations are performed within the windowing.
[0171] In sequence S430 'of the code replacing the code sequence S430, the x_stack stack is prepared by reshaping the x_win_orig vector. However, because the X_win_orig vector contains only 320 elements, compared to the corresponding vector from Fig. 9a containing 640 elements, the x_stack matrix is only a 64-5 element matrix.
[0172] The character substitution code S440 and the stacking code S450 sequence are identical in both embodiments of Figs. 9a and 9b, in addition to a reduced number of elements (320 compared with 640).
[0173] In sequence S460 'of the code replacing the sequence S460, the odd unified Fast Fourier transform (FFT) is implemented for window data, which is quite similar to the transformation of the S460 sequence of the code in Fig. 9a. However, again, due to the reduced number of output audio subbands, the result of the fast Fourier transform, the multiplication of elements dependent on the x_stack stack element and the complex exponential function of the argument (-i · π · n / 64) is provided in the temp vector, the index n being it is in the range between 0 and 63.
Then, in the modified code sequence S470 ', the final chamfering is performed by defining the variable m = (32 + 1) / 2 and by generating the output vector y according to equation (26), the index k covering only the range from 1 to 32 and wherein the number 128, appearing as the argument of the combined exponential function, is replaced by the number 64.
In the final code sequence S480 ', the state buffer is shifted by 32 elements in the case of the embodiment shown in Fig. 9b, wherein in the corresponding code sequence S480, the buffer is shifted by 64 elements.
[0176] Fig. 10a shows a MATLAB script illustrating an embodiment of an embodiment of the present invention in the form of a method relating to a synthesis filter bank of complex values for 64 subbands. The script shown in Fig. 10a defines the function of ILDFB80 to which the x vector representing the audio subbands 320 of Fig. 2a is supplied and the state "state" is provided as input parameters. The name ILDFB80 indicates that the defined function is an inverted low-delay filterbank corresponding to 8 blocks of audio data from the past and 0 blocks from the future. The function provides a vector y and a new or redefined state vector "state" at the output, wherein the vector y corresponds to block 410 of the time domain audio samples of Fig. 2a.
In the code sequence S500, a pre-chamfering is performed in which the variable m = (64 + 1) / 2 is defined as well as the temperature vector. The temperature (n) elements of the temperature vector are defined according to the equation of temp (n) = j · x (n) · exp (2i · * (n - 1 + |) · - &), <sub>(2</sub>7) where the dash above the vector element x (n) and the conj () function represents a complex conjugate, exp () represents a complex exponential function, and represents an imaginary unit, and n is an index in the range from 1 - to 64.
In the S510 sequence of the code, the temperature vector is extended to the matrix containing the elements of the temperature vector in the first column, and in the second column the complex conjugate of the inverted temperature vector relative to the order of the elements defined by the vector index. Hence, in the S510 sequence of the code, odd symmetry of the temperature matrix is established based on the vector temp.
[0179] In the S520 sequence, an unequal Fast Fourier Transform (FFT) code is implemented based on the temperature matrix. In this code sequence, the real part of the multiplication of the element dependent inverted Fourier transform of the temperature matrix by the exponential function of the argument (i · π / 128 ) is implemented and output to the vector y_knl, the index n being in the range from 0 to 127.
[0180] In the sequence S530, the data extension is formed and the character change alternately. To obtain this, the order of the elements of the vector y_knl is inverted and at the same time the change of the sign is carried out. Next, the matrix tmp is defined, comprising the first, third and fifth columns of the vector y-knl, wherein the second and fourth columns contain the vector y-knl with the changed sign.
In the code sequence D540, the window coefficients stored in the LDFB80_win vector are first copied to the win_ana vector. Next, the coefficients of the synthesis window are determined based on the analysis window coefficients stored in the win_a vector by generating a reverse version of the analysis window function according to the win _ syn (n) = win __ ana (N · T '- η) where N · T is the total number of window coefficients, and n is the index of window coefficients.
[0182] In the code sequence S550, a synthesis window is applied to the tmp vector by the multiplication of the vector element by the function of the synthesis window. In the S560 sequence, the buffer code is updated by setting the vector state elements with indices 577 to 640 to 0 and by adding the contents of the windowed vector tmp to the state vector state.
[0183] In the S570 sequence of the code, the output vector s including the time-domain audio samples is derived from the state vector by acquiring vector state elements by acquiring state vector elements with indexes 1 to 64.
[0184] In the code sequence S580, the final sequence of the function code shown in Fig. 10a, the state vector is shifted by 64 elements, such that elements with indices 65 to 640 are copied to the first 576 elements of the state vector.
[0185] Fig. 10b shows a MATLAB implementation script according to an embodiment of the present invention in the form of a synthesis filter bank with complex values for 32 subband values. The function name defined by the script shown in Fig. 10b illustrates this, because the defined function is called ILDFB80_32 indicating that the defined function is an inverted low delay filter bank for 32 bands with a bookmark of 8 blocks from the past and a bookmark of 0 blocks from the future.
[0186] As discussed in the comparison of embodiments shown in Figs. 9a and 9b, the implementation according to the script of Fig. 10b is also closely related to the implementation of a 64-band synthesis filter bank according to Fig. 10a. As a result, the same vectors that are delivered to the function and output by the function are, however, which contain only half of the elements compared to the embodiment of Fig. 10a. The implementation for a 32-band synthesis filterbank for 32 bands is different from the 64-sub-version shown in Fig. 10a mainly in terms of two aspects. Sequences S500, S510, S520, Ξ53β, S560, S570 and S580 code are replaced by code sequences, in which the number of elements to be addressed and the next number associated with the parameter elements are divided by 2. In addition,
In the sequence S500 'of the code replacing the sequence S500 of the code, the variable m is defined as m = (32 + 1) / 2 and the vector temp is defined according to equation (27), the index n covering only the range from 1 to 32 and where the factor 1/128 is replaced by the factor 1/64 in the argument of the exponential function.
[0188] Accordingly, in the sequence S510 'of the code replacing the code sequence S510, the index range covers only the indexes 32 of the elements containing the temperature vector. In other words, the index covers only values from 1 to 32. Correspondingly, in the sequence S520' of the code , replacing the code sequence S520, the argument of the exponential function is replaced by (i · π · n / 64), where the index n is in the range from 0 to 63. As part of the code S530 ', the index range is also reduced by factor 2 in comparison with the code sequence S530.
[0189] The code sequence S542, which replaces the code sequence S540 of Fig. 10a, also copies the window function stored in the LDFB80_win vector to the win_ana vector and generates a time-reversed version of the win_syn according to equation (28). However, the execution code sequence S542 shown in Fig. 10b additionally comprises an interpolation step according to equation (15), in which each element of a redefined win_syn vector comprises window coefficients of the synthesis window function, linear interpolation of two successive window coefficients of the original function of the synthesis window.
[0190] The code sequence S550, the use of the tmp vector window and the replacement of the tmp elements with their windowed version, is code identical in direct comparison of the respective code sequences in Figs. 10a and 10b. However, due to the smaller size of the tmp vector in the embodiment of Fig. 10b, during implementation, only half of the number of multiplication operations are performed.
[0191] Also within the sequence S560 'S570' and S580 'of the code, replacing respectively the sequences S560, S570 and S580 of the code, the indexes 640 and 64 are replaced by 320, and 32, respectively. Therefore, these three final code sequences differ only from the execution code sequence shown in Fig. 10a in terms of the size of the tmp and y state vectors.
[0192] As the exemplary embodiments described so far, the analysis windowing module as well as the synthesis windowing module are adapted for windowing respective time-domain samples contained in respective frames by multiplying them depending on the element by window coefficients of the window function.
[0193] Before a more detailed description of a window function that can be used, for example, as a function of a synthesis window and as a function of the analysis window in its inverted version, the advantages of the embodiments of the present invention will be outlined in greater detail, in particular in the light of implementation in within the tool or SBR system shown in Figs. 5 and 6.
[0194] Among the benefits, embodiments of the present invention and systems comprising more than one embodiment of the present invention can offer a significant reduction in delay with other filter banks. However, this low delay property will be presented in more detail in the context of Figures 13 and 14. As one important aspect in this context, it should be noted that the length of the window function, to put it another way, the number of window coefficients to be applied to the frame or block of samples in time domain is independent of the delay.
[0195] Additionally, as will be outlined in more detail in the context of Figs. 17 and 18, in terms of psychoacoustics, the embodiments of the present invention often utilize the temporal masking properties of the human ear better than many other filter banks. In addition, as will be outlined in the context of FIGS. 15, 16 and 19, the embodiments of the present invention offer an excellent frequency response.
[0196] Also, many filter banks according to the present invention can achieve an excellent reconstruction if the analysis filter bank and the synthesis filter bank are interconnected. In other words, the embodiments of the present invention not only offer audible indistinguishable results compared to the entry of such an interconnected analysis filter bank and synthesis filter bank, but (apart from quantization errors, computational rounding effects and subsequent effects caused by the necessary discretization) identical output in compared to the entrance.
[0197] Integration into the SBR module of the filter banks of the present invention can be easily obtained. When typically SBR modules operate in dual-band mode, the complex low-delay filter banks according to embodiments of the present invention are capable of providing excellent single-range reconstruction, while the original SBR QMF filter banks are only capable of providing nearly perfect reconstruction. In the two-band mode, the 32-band version of the impulse response is obtained by linear interpolation also referred to as smaller sampling of two adjacent branches or window coefficients of the 64-band pulse response or window function, as explained in the context of Fig. 3.
[0198] In the complex filterbank implementation, a significant reduction in the analysis (or synthesis) delay can be obtained for critically sampled filter banks in which the sampling or processing frequency corresponds to the limit frequency according to the Nyquist-Shannon theorem. In the case of implementing a real-valued filter bank, an efficient implementation can be obtained using optimized algorithms, such as illustrated in the context of MATLAB implementation shown in Figs. 9 and 10. These embodiments can be, for example, used for low-power mode SBR tools as described in the context of Figs. 5 and 6.
[0199] As outlined in the context of Figures 5 and 6, it is possible to obtain a further reduction regarding the delay in the SBR system by using a low complex delay filter bank according to an embodiment of the present invention. As previously outlined, in the 610 SBR decoder shown on
Fig. 5, bank QMF analysis filter 620 is replaced by a complex low delay filter bank (CLDFB) according to an embodiment of the present invention. This substitution can be made in a computational manner by preserving the number of bands (64), the length of the impulse response (640) and by using complex modulation. The delay obtained by this tool is minimized in such a way as to achieve a total delay low enough for two-way communication without sacrificing the achievable level of quality.
[0200] In comparison, for example, with a system comprising MDCT and MDST to form an MDCT system with complex values, the embodiment of the present invention offers a much better impulse response. In comparison with the QMF filter bank, for example, as used today in MPEG-4 SBR, a system comprising one or more filter banks according to embodiments of the present invention provides a much lower delay.
[0201] Even compared to the low-delay QMF filter bank, the embodiments of the present invention offer the advantage of excellent reconstruction combined with a low delay. The benefits of the perfect reconstruction properties as opposed to the almost perfect reconstruction of QMF filter banks are as follows. In the case of almost perfect reconstruction, high stopband suppression is necessary to adequately suppress aliasing. This limits the possibility of a very low delay in the filter design. In contrast, with the embodiment of the present invention, it is now possible to independently design the filter so that high bandpass damping is not necessary to suppress aliasing to low enough levels. The bandpass suppression must be low enough to allow for reduced aliasing sufficient for the desired use in signal processing. In this way, a better compromise can be obtained towards the low delay in filter design.
[0202] Fig. 11 shows a comparison of a window function 700 which may, for example, be used in an embodiment of the present invention together with the sine window function 710. The window function 700, which is also called the CMLDFB window (CMLDFB = complex modulated low-delay filterbank) of "synthesis", contains 640 window coefficients based on the values given in the Appendix 1 table. the size of the window function should be noted that general gain factors or damping factors for adjusting the amplitude of the windowed signal are not included below. The window functions may, for example, be normalized in terms of values corresponding to the delay means as outlined in the context of Fig. 13 or with respect to the value of n = N, n = N-1 or n = N = 1, where N is the block length, and n is the index of window coefficients. For comparison, the sine window function 710 is only defined for 128 samples and is, for example, used for the MDCT or MDST module.
[0203] However, depending on the details of the implementation, to account for the window coefficients based on the values given in the tables of appendices 1 and 3, additional changes of the sign relative to window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be considered (factor multiplication (-1) )) should be considered in accordance with equation (16a) and (16b).
[0204] Before discussing the differences between two window functions 700, 710, it should be noted that both window functions include only window coefficients with real values. In addition, in both cases, the absolute value of the window coefficient corresponding to the index n = 0 is less than 0.1. In the case of the CMLDFB window 700, the corresponding value is even less than 0.02.
[0205] When considering two window functions 700, 710 in terms of their sets of definitions, there are several evident differences. When the sine window function 710 is symmetrical, the window function 700 exhibits asymmetrical behavior. For a clearer definition of this, the sine window function is symmetric because there exists a value of n0 with real values relative to all n real numbers, so that the window function 700 is defined for (n0 + n) and (n0-n), the dependency
Μ<sup>η</sup>ο - <sup>n</sup>H = K<sup>n</sup>o + <sup>n</sup>) (29) is satisfied with the desired margin (ε> 0, the absolute value of the difference of expressions on both sides of the equation (29) is less than or equal to ε), w (n) represents the window coefficient corresponding to the index n. In the case of a sine window the corresponding index n0 is exactly in the middle of the two extremely upper window coefficients. In other words, for the sine window 710, the index n0 = 63.5. The sine window function is defined for indices n = 0, ..., 127.
[0206] In contrast, window function 700 is defined for the set of indexes n = 0, ..., 639. The window function 700 is clearly asymmetric in the sense that for all real numbers n there is always at least one real number so that (n0 + n) and (n0-n) belong to the window function definition set, for which the inequality p (n<sub>0</sub> - nj. * p (n<sub>0</sub> + nj <sub>(3Q)</sub> is fulfilled with (almost deliberately) possible to define a reserve (ε> 0, the absolute value of the difference of expressions on both sides of the equation (29) is greater than or equal to ε), again, w (n) is the window coefficient corresponding to index n.
[0207] Further differences between the two window functions, both of which relate to the block sizes N = 64 samples, mean that the maximum value of the window function 700 is greater than 1 and is acquired for indexes in the range
Ν <η <2Ν (31) for the synthesis window. In the case of the window function 700 of Fig. 11, the maximum value adopted is greater than 1.04, assumed for the index n = 77 samples. In contrast, the maximum value of the sine window 710 is less than or equal to 1, and it is taken at n = 63 and n = 64.
[0208] However, also window function 700 assumes an approximate value of 1 with the sample indices around n = N. More specifically, the absolute value or the same value of the coefficient w (N-1) of the window corresponding to the index n = N-1 is less than 1, while the absolute value or the same value of the coefficient w (n) of the window corresponding to the index n = N is greater than 1 In some embodiments of the present invention, these two window coefficients fulfill dependencies
0.99 <w (N - l) <1.0
1.0 <w (n) <1.01 · (32) which is the result of optimization of the filter bank's audio quality according to embodiments of the present invention. In many cases, it is desirable that the coefficient w (0) of the window should have an absolute minimum value. In this case, the determinant of window coefficients p (o) · w (2N - l) - w (w - l) · w (w) |? 1 (33) should be as close as possible to 1 for audio quality, which is optimized for in terms of possible parameters. The determinant mark, given by equation (33), can, however, be freely chosen. The result of the fact that the coefficient w (0) of the window is smaller or approximately equal to 0, the product w (N-1) · w (N) or its absolute value should be possible nearest to +/- 1. In this case, the coefficient w ( 2N-1) the window can then be selected almost freely. Equation (33) is the result of the use of the zero delay matrix technique described in the "New Framework for Modified Perfect Reconstruction Filter Banks" by GDT Schuller and MJT Smith, IEEE Transactions on Signal Processing, vol. 44, No. 8, August 1996.
[0209] Additionally, as will be outlined in more detail in the context of Fig. 13, the window coefficients corresponding to the N-1 indexes are included in the middle of the modulation core and therefore correspond to a sample having a value of approximately 1.0 and which coincide with the bank delay filters defined by the prototype filter function or window function.
[0210] The synthesis window function 700 shown in Fig. 11 additionally exhibits oscillating behavior with strictly monotonic increasing window coefficients from the window coefficient window coefficient coefficient corresponding to the index (n = 0) used for windowing the last audio sample in the time domain up to the window coefficient containing the highest achievable absolute value from all window coefficients of function 700 of the synthesis window. Naturally, in the case of an inverse analysis window function,
[0211] As a result of the oscillatory behavior, the course of function 700 of the synthesis window begins with a window coefficient corresponding to the index n = 0 having an absolute value less than 0.02 and an absolute value of the window coefficient corresponding to the index n = 1 lower than 0.03, assuming a value in an approximation of 1 at the index n = N, assuming a maximum value above 1.04 at the index according to equation (31), assuming a next value approximately 1 at the index n = 90 and 91, the first sign change at the index values n = 162 in = 163 , assuming a minimum value less than -0.1 or -0,12755 at the index of approximately n = 3N and the next change of the sign at the index values n = 284 and n = 285. However, function 700 of the synthesis window can additionally contain further character substitutions at subsequent n index values.
[0212] The oscillatory behavior of function 700 of the synthesis window is similar to the behavior of strongly suppressed oscillations, as illustrated by a maximum value of about 1.04 and a minimum value of about -0.12. As a result, over 50% of all window coefficients contain absolute values less than or equal to 0.1. As outlined in the context of the embodiments of Figs. 1 and 2a, the window function includes a first group 420 (or 200) and a second group 430 (or 210), the first group 420 including the first subsequent portion of the window coefficients and the second group 430 contains another second part of window coefficients. As previously outlined, the sequence of window coefficients contains only the first group of 420 window coefficients and the second group of window coefficients 430, wherein the first group contains exactly the first consecutive sequence of window coefficients and wherein the second group 430 comprises exactly the second subsequent portion of the window coefficients. Thus, the terms first group 420 and first part of window coefficients, as well as the terms second group 430 and second part of window coefficients can be used synonymously.
[0213] More than 50% of all window coefficients having an absolute value less than or equal to 0.1 are contained in the second group or second portion of window coefficients 430 due to the strongly suppressed behavior of the window function 700. In addition, also more than 50% of all window coefficients included in the second group or the second part 430 of the window coefficients have absolute values less than or equal to 0.01.
[0214] The first portion 420 of the window coefficients comprises less than one third of all window coefficients of the sequence coefficients of the window. Accordingly, the second portion 430 of the window coefficients comprises more than two-thirds of the window coefficients. For the total number of T blocks to be processed in one of the frames 120, 150, 330, 380 of more than 4 blocks, the first portion typically comprises 3/2 · N window coefficients, where N is the number of samples in the time domain of one block. Accordingly, the second part includes the rest of the window coefficients or, to be more exact, (T-3/2) N window coefficients. In the case of T = 10 blocks per frame, as shown in Fig. 11, the first part comprises 3/2 · N window coefficients, while the second portion 210 comprises 8.5 · N window coefficients. For the block size N = 64 audio samples in the time domain per block, the first part contains 96 window coefficients, while the second part contains 544 window coefficients. The function of the synthesis window 700, as shown in Fig. 11, assumes an approximate value of 0.96 at the boundary of the first part and the second part at the index of about n = 95 or 96.
[0215] Regardless of the number of window coefficients included in the first portion 420 and second portion 430, the energy value or total energy value of the respective window coefficients vary widely between each other. The energy value defined by
Ε η
(34) wherein w (n) is the window coefficient, and index n, against which the sum in equation (34) is evaluated, corresponds to the indices of the respective parts 420, 430, to the entire set of window coefficients or to any other set of window coefficients to which the corresponding energy values E. Despite the considerable difference in window coefficients, the energy value of the first part 420 is equal to or greater than 2/3 of the total energy value of all window coefficients. Correspondingly, the energy value of the second portion 430 is less than or equal to 1/3 of the total energy value of all window coefficients.
[0216] To illustrate this, the energy value of the first portion 420 of the window coefficients of the window function 700 is approximately 55.85, and the energy value of the window coefficients of the second portion 430 is approximately 22.81. The total energy value of all windows window function coefficients 700 is approximately 78.03 so that the energy of the first portion 420 is approximately 71.6% of the total energy value and the energy value of the second portion 430 is approximately 28.4% of the total energy value. all window coefficients.
[0217] Naturally, equation (34) can be represented in a version normalized by dividing the energy values E by the normalization factor E0, which in principle can be the energy value. The normalization factor E0 may, for example, be the total energy value of all window coefficients of window coefficient coefficients calculated in accordance with equation (34).
[0218] Based on the absolute values of the window coefficients or based on the energy values of the corresponding window coefficients, the center point or "center of mass" of the window coefficient sequence may also be determined. The center of mass or the center point of the window coefficient sequence is a real number and is usually in the index range of the first portion 420 of the window coefficients. For appropriate frames containing more than four blocks of samples (T> 4) audio in the time domain, the center of mass based on absolute values of window coefficients or center of mass based on energy values of window coefficients is less than 3/2 · N. In other words in the case of T = 10 blocks per frame, the center of mass lies clearly within the index region of the first portion 200.
[0219] A center of mass based on the absolute values of window coefficients w (n) is defined according to
Ν-τ-ι '.
Σ<sup>n</sup> · KM n = ......
<sup>n</sup>ca NJ-1 (35)
Σ M<sup>n</sup> n = 0 and the center of mass in the light of the energy values of coefficients w (n) of the window is defined in accordance with
NTL
Σ<sup>n</sup> · KM<sup>2</sup> n = _ ** ce NTl
ZkW n'0 (36) wherein N and T are positive integers indicating respectively the number of audio samples in the time domain per block and the number of blocks per frame. Naturally, the midpoints according to equations (35) and (36) can also be calculated in relation to a limited set of window coefficients by appropriate exchange of the boundaries of the above sums.
[0220] For the function 700 of the window shown in Fig. 1, the center of mass nca of the vapor on absolute values of coefficients w (n) of the window is equal to nca ~ 87.75 and the center point or center of mass nce with respect to energy values of coefficients w ( n) windows is nce ~ 80,04. Since the first portion of the window function coefficients of window function 700 includes 96 (= 3/2 · N; N = 64) window coefficients, both midpoints are clearly in the first part of 200 window coefficients, as outlined above.
[0221] The coefficients in (n) windows of the window function 700 are based on the values given in the table in annex 1. However, in order to obtain, for example, the filter bank's low delay properties previously drawn up, it is necessary to perform window functions as accurately as they give window coefficients in annex table 1. In many cases, it is more than sufficient if window coefficients of a window function containing 640 window coefficients to satisfy any of the dependencies or equations given in the annexes 2 to 4. The window coefficients or filter coefficients given in the annex 1 table represent favorable values that can be adapted in accordance with equations (16a) and (16b) in some implementations. However, as indicated, for example, in the following tables in the following annexes, the positive values may change to the second, third, fourth and fifth digits, so that the resulting window filters or functions still have the advantages of embodiments of the present invention. However, depending on the implementation details, to obtain window coefficients based on the values given in the tables of appendices 1 and 3, additional changes of the sign relative to window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be considered (multiplication by factor (-1)) should be considered in accordance with equations (16a) and (16b).
[0222] Naturally, subsequent window functions comprising a different number of window coefficients can equivalently be defined and used within the embodiments of the present invention. In this context, it should be noted that both the number of time-domain audio samples per block and block distribution with respect to past and future samples can vary over a wide range of parameters.
[0223] Fig. 12 shows a comparison of a combined modulated bank filter window 700 (CMLDFB window) shown in Fig. 11 and an original QMF prototype filter 720 used, for example, in an SBR tool according to MPEG standards. As shown in Fig. 11, the CMLDFB window 700 is again a synthesis window according to an embodiment of the present invention.
[0224] Although the window function 700 according to the embodiment of the present invention is clearly asymmetric, as defined in the context of equation (30), the original QMF prototype filter 720 SBR is symmetric with respect to indexes n = 319 and 320 because both the window function 700 as and the prototype filter 720 SBR QMF are each defined with reference to each of the 640 indexes. In other words, with reference to equation (29), the "index value" n0 representing the index of the center of symmetry is given by n0 = 319,5 for the prototype filter 720 SBR QMF.
[0225] In addition, due to the symmetry of the prototype filter 720 SBR QMF, also the center points nce and nce according to equations (35) and (36), respectively, are identical to the center of n0 symmetry. The value of the prototype energy of the 720 SBR QMF filter is 64.00 because the prototype filter is an orthogonal filter. In contrast, the clearly asymmetric function 700 of the window contains an energy value of 78.0327, as was previously outlined.
[0226] The following sections of the description will consider SBRs sketched in the context of Figures 5 and 6, wherein the SBR decoder 610 includes embodiments of the present invention in the form of an analysis filter bank as a filter bank 620 and an embodiment of the present invention in the form of a bank synthesis filters for the bank 640 synthesis filters. As will be outlined in more detail, the total delay of the analysis filterbank of the present invention utilizing the window function 700 shown in Figs. 11 and 12 includes a total delay of 127 samples, while the original tool based on the QMF SBR prototype filter results in a total delay 640 samples.
[0227] Replacing filter banks QMF in an SBR module, e.g. in a SBR decoder 610, into a low-delay filter bank with complex values (CLDFB) leads to a reduction in the latency from 42 ms to 31.3 ms without any degradation of the audio quality or additional computational complexity. In the case of a new filter bank, both the standard SBR mode (high-quality mode) and the low-power mode are operated using only filter banks with real values, as shown in the description of the examples with reference to Figures 7 to 10.
[0228] In particular in the field of telecommunications and bi-directional communication, the low delay is of great importance. Although the improved AAC is already capable of generating a 42 ms delay, small enough for communications applications, its algorithm delay is still higher than the low latency AAC core codec, which is capable of obtaining latencies reduced to 20 ms and other telecommunications codecs. In the 610 SBR decoder, the QMF analysis and synthesis stages still introduce a reconstruction delay of 12 ms. A promising approach to reducing the delay is to use a low delay filter bank technique according to an embodiment of the present invention and to replace the current QMF filter banks by a suitable low latency version according to an embodiment of the present invention.
[0229] For use in the 610 SBR module, the new filter banks according to embodiments of the present invention, which are also called CLDFBs, are designed to be as similar as possible to the originally used QMF filter banks. This includes, for example, the use of 64 subbands or bands, the same length of pulse responses, and compatibility with dual band modes used in SBR systems.
[0230] Fig. 13 shows a comparison of a CLDFB window shape 700 according to an embodiment of the present invention and an original QMF SBR prototype filter 720. In addition, it represents the delays of modulated filter banks that can be determined by analyzing the delay of the overlap introduced by the prototype filter or window function in addition to the delay of the modulation core mapping having the length of N samples in the case of a DCT-IV based system. The situation shown in Fig. 13 refers again to the case of a synthesis filter bank. The window function 700 and the prototype filter 720 also represent impulse responses of the prototype synthesis filters of the two involved filter banks.
[0231] Regarding the delay analysis for both the SBR QMF filter bank and the proposed CLDFB according to the embodiment of the present invention, only the overlap in the right and the left of the modulation core, respectively, introduces an additional delay in the analysis and synthesis.
[0232] For both filter banks, the modulation core is based on DCT-IV introducing a delay of 64 samples, which is indicated in Fig. 13 as a delay of 750. In the case of a QMF prototype filter 720, due to symmetry, a delay of modulation core 750 is provided symmetrically relative to the center of mass or midpoint of the corresponding filter prototype function 720, as shown in Fig. 13. The reason for this behavior is that the SBR QMF filter bank must be filled until the prototype filter function 720 having the most significant share in terms of corresponding values The energy value of the prototype filter will be included in the processing. Due to the shape of the prototype filter function 720, this requires
[0233] To illustrate this, starting with a fully initialized buffer of the corresponding QMF SBR filter bank, the buffer must be filled to the point at which the data processing will result in the processing of relevant data, requiring that the relevant window function or prototype filter function has a significant contribution. In the case of the prototype function of the SBR QMF filter, the symmetrical shape of the prototype filter 720 provides a delay that is of the center of mass or midpoint of the prototype filter function.
[0234] However, since the delay introduced by the core of the system modulation based on DCT-IV with N = 64 for samples is always present and the system also includes a delay of one block, it can be seen that the synthesis prototype for SBR QMF introduces a overlap delay of 288 samples.
[0235] As mentioned above, in the case of the synthesis filter bank referred to in Fig. 13, this additional tab 760 on the left causes a delay whereas the tab 770 almost on the side refers to past samples and therefore does not introduce an additional delay in case of a synthesis filter bank.
[0236] In contrast, starting with a fully initialized CLDFB buffer according to an embodiment of the present invention, the synthesis filter bank, as well as the analysis filter bank, are capable of delivering "significant" data earlier compared to the SBR QMF filterbank, due to the shape of the function window. In other words, thanks to the shape of function 700 of the analysis and synthesis window, samples processed by window functions indicating significant shares are available earlier. As a result, the synthesis prototype or synthesis function of the CLDFB synthesis window introduces only the delay of the overlap of 32 samples, taking into account the delay already introduced by the core 750 of the modulation.
[0237] The same delay is entered by the analysis filter bank or the analysis prototype function. The reason is that the analysis filter bank is based on a reverse version of the function of the synthesis window or prototype function. In this way, the tab delay is entered on the right side having the same tab size as the synthesis filter bank. Thus, in the case of the original prototype QMF filter, a delay of 288 samples is also introduced, while in the analysis filter bank according to the embodiment of the present invention only 32 samples are introduced as a delay.
[0238] The table shown in Fig. 14a shows a general outline of the delay with different stages of modification with the adopted frame length of 480 samples and a sampling rate of 48 kHz. In a standard configuration including the AAC-LD codec along with the standard SBR tool, the MDCT and IMDCT filter banks in the dual-band mode cause a 40-ms delay. In addition, the QMF tool itself causes a 12 ms delay. Additionally, due to the SBR tab, another 8 ms delay is generated, so that the total delay of this codec is in the range of 60 ms.
[0239] For comparison, the AAC-ELD codec comprising the low-latency versions of MDCT and IMDCT generates a 30-ms delay in a two-band mode. Compared to the original SBR QMF filter bank, the use of a low complex delay filter bank according to an embodiment of the present invention results in a delay of only 1 ms compared with 12 ms of the original QMF tool. By avoiding the SBR tab, you can avoid the additional overlap of 8 ms for a simple AAC-LD combination and the SBR tool. Accordingly, the improved low latency AAC codec is capable of a total algorithmic delay of 31 ms instead of 60 ms for a previously drawn simple combination. In this connection, it can be seen
[0240] The table in Fig. 14b shows another general outline of the total codec latency caused by the original and proposed versions of the filter bank in the system shown in Figs. 5 and 6. The data and values given in Fig. 14b are based on a sampling rate of 48 kHz and size core coder frame 480 samples. Due to the dual-band approach in the SBR system shown and discussed in Figs. 5 and 6, the core coder actually operates at a sampling rate of 24 kHz. Because the frame delay of 64 samples for the modulation core is already introduced by the core coder, it can be subtracted from the delay value of the independent two filter banks described in the context of Fig. 13.
[0241] The table in Fig. 14b emphasizes that it is possible to reduce the overall delay of the improved low latency AAC codec comprising the low latency version of MDCT and IMDCT (LD MDCT and LD IMDCT). Although a total 42-ms algorithm delay can only be obtained by using the low-latency version of the MDCT and IMDCT as well as the original QMF filter banks, by using low-complex filter banks according to embodiments of the present invention, instead of the conventional QMF filter banks, total latency algorithmic can be significantly reduced to only 31.3 ms.
[0242] To assess the quality of filter banks according to embodiments of the present invention and systems comprising one or more filter banks, listening tests were conducted from which it can be concluded that filterbanks according to embodiments of the present invention maintain the AAC-ELD audio quality at the same level. and do not introduce any degradation, either in complex SBR mode or in low-power SBR mode with low delay. Accordingly, filter banks with an optimized delay according to embodiments of the present invention do not introduce any burdens for audio quality, although they are capable of reducing the delay by more than 10 ms. For intermediate items, you can even observe that you can even get a small but statistically insignificant improvement.
[0243] In order to further verify that the reduced sampling for the 32band filter bank according to the embodiment of the present invention works equally well for the filter banks of the present invention compared to the QMF filter banks, the following evaluation was performed. First, the logarithmic sine search was analyzed with a 32-band filter bank with reduced sampling, with 32 upper bands, zero-initialized, added. Then, the result was synthesized by a 64-band filter bank, the sampling was reduced again and compared to the original signal. The use of a conventional QMF SBR prototype filter leads to a signal-to-noise ratio (SNR) of 59.5 dB. The filter bank of the present invention, however, obtains an SNR of 78.5 dB, which shows
[0244] In order to demonstrate that this optimized for delay, the asymmetric bank filter approach used in the embodiments of the present invention provides added value compared to a classical symmetrical prototype filter bank, asymmetric prototypes will be compared below with symmetric prototypes having the same delay.
[0245] Fig. 15a shows a comparison of the frequency response of a far-field illustration of a filter bank according to the present invention using a low latency window (graph 800) compared to a filter bank frequency response using a sine window with 128 branch lengths ( chart 810). Fig. 15b shows an enlargement of the near-field frequency response of the same filter bank using the same window functions as previously outlined.
[0246] A direct comparison of two graphs 800, 810 shows that the frequency response of a filterbank using a low delay filterbank according to an embodiment of the present invention is much better than the corresponding frequency response of a filter bank using a sine window having 128 branches having the same delay.
[0247] Also, Fig. 16a shows a comparison of different window functions with a total delay of 127 samples. A filter bank (CLDFB) with 64 bands has a total delay of 127 samples including latency framing and tab lag. A modulated filter bank with a symmetrical prototype and the same delay would therefore have a prototype length of 128, as already illustrated in the context of Figs. 15a and 15b. For these filter banks with 50% overlap, such as, for example, MDCT, sine windows or windows based on the KaiserBessel window generally offer a good choice for prototypes. Hence, in Fig. 16a, a general outline of the frequency response of a filter bank using a low latency window as a prototype according to the present invention was compared with the frequency responses of alternative symmetrical prototypes with the same delay. FIG. 16a shows, in addition to the frequency response of the filter bank according to the present invention (graph 800) and the frequency response of a filterbank using a sinus window (diagram 810), as already shown in Figs. 15a and 15b, two KBD windows on the basis of α = 4 parameters ( graph 820) and α = 6 (graph 830). Both Fig. 16a and enlargement Fig. 16a shown in Fig. 16b clearly show that a much better frequency response can be obtained by means of a filter bank according to an embodiment of the present invention having an asymmetric window function or a prototype filter function with the same delay. 15a and 15b, additionally two KBD windows based on the parameters α = 4 (graph 820) and α = 6 (graph 830). Both Fig. 16a and enlargement Fig. 16a shown in Fig. 16b clearly show that a much better frequency response can be obtained by means of a filter bank according to an embodiment of the present invention having an asymmetric window function or a prototype filter function with the same delay. 15a and 15b, additionally two KBD windows based on the parameters α = 4 (graph 820) and α = 6 (graph 830). Both Fig. 16a and enlargement Fig. 16a shown in Fig. 16b clearly show that a much better frequency response can be obtained by means of a filter bank according to an embodiment of the present invention having an asymmetric window function or a prototype filter function with the same delay.
[0248] To illustrate this advantage more generally, in Figure 17, two filter bank prototypes are compared with delay values other than in the previously described filter banks. When the filter banks considered in Figs. 15 and 16 have a total delay of 127 samples, corresponding to a block of 8 blocks in the past and 0 blocks in the future (CLDFB 80), Fig. 17 shows a comparison of the frequency response of two different filter bank prototypes with the same delay 383 samples. More specifically, FIG. 17 shows the frequency response of an asymmetric prototype filterbank (chart 840) which is based on the tab 6 blocks of time-domain samples in the past and 2 blocks of time-domain samples into the future (CLDFB 62). Additionally, Fig. 17 also shows the frequency response (graph 850) of the corresponding symmetrical prototype filter function, also having a delay of 383 samples. It can be seen that with the same delay value, an asymmetric prototype or window function achieves a much better frequency response than a filter bank with a symmetrical window function or a symmetrical prototype filter. This indicates the possibility of obtaining a better compromise between delay and quality, as stated earlier.
[0249] Fig. 18 shows the effect of temporarily masking a human ear. When the tone or tone appears at the time indicated by line 860 in Fig. 18, the masking effect associated with the pitch or pitch frequency and adjacent frequencies increases approximately 20 ms before the actual sound begins. This phenomenon is called pre-emptive masking and is one aspect of the human-psychoacoustic properties of the human ear.
[0250] In the situation illustrated in Fig. 18, the sound remains audible for about 20 ms until the time indicated by line 870. At this time, the human ear's masking system is active, which is also referred to as simultaneous masking. After the end of the sound (indicated by line 870), frequency masking in the frequency of the adjacent tone slowly disappears over a period of about 150 ms, as shown in Fig. 18. This psychoacoustic phenomenon is also referred to as final masking.
[0251] Fig. 19 shows a comparison of pre-echo signaling behavior of a signal encoded by a conventional HE-AAC and a HE-AAC-based filter-based bank using a low-delay filter bank (CMLDFB) according to an embodiment of the present invention. Fig. 19a shows the original castanet timing signals that have been processed using a system comprising the HEAAC codec (HE-AAC = high performance audio advanced codec). The result of the operation based on the conventional HE-AAC is shown in Fig. 19b. Direct comparison of two signals, the original time signal and the output signal from the HE-AAC codec shows that
[0252] Fig. 19c shows the output of a HE-AAC containing system based on filter banks comprising CMLDFB windows according to an embodiment of the present invention. The same original time signals indicated in Fig. 19a and processed using the filter banks according to the embodiment of the present invention show a significant reduction in the pre-echo effect just before the start of the castanel signal indicated by the arrow 890 in Fig. 19c. Due to the pre-masking phenomenon described in the context of Fig. 18, the pre-echo phenomenon marked with arrow 890 in Fig. 19c will be much better masked than pre-echo phenomena marked with arrow 880 in the case of a conventional HE-AAC codec. Hence, the pre-filter echo property of filter banks according to the present invention, which is also the result of a significantly reduced delay compared to conventional filter banks, causes the output signal to be much better suited to the timing and psychoacoustic properties of the human ear. As a result, as already indicated in the description of the listening tests, the use of filter banks according to an embodiment of the present invention may even lead to an improvement in the quality caused by the reduced delay.
[0253] Embodiments of the present invention do not increase computational complexity compared to conventional filter banks. Low-delay filter banks use the same filter length and the same modulation mode as, for example, QMF filter banks for SBR systems, so that the computational complexity does not increase. In terms of memory requirements due to the asymmetric nature of prototype filters, ROM requirements (read-only memory) for the synthesis filter bank are increased by approximately 320 words for the filter bank based on N = 64 samples per block and T = 10 blocks per frame . In addition, in the case of an SBR-related system, the memory requirements are increased by a further 320 words if the analysis filter is stored separately.
[0254] However, since the current ROM requirements for the AAC-ELD core are approximately 2.5 k words (one thousand words) and for the implementation of SBR a further 2.5 k words, the ROM requirements are only moderately increased by about 10%. As a potential trade-off between memory and complexity, if low memory consumption is the most important, linear interpolation can be used to generate an analysis filter from a synthesis filter, as outlined in the context of Fig. 3 and equation (15). This interpolation operation increases the number of necessary instructions by only approximately 3.6%. In this regard, replacing conventional QMF filter banks within SBR modules by low delay filter banks according to embodiments of the present invention,
[0255] Embodiments of the present invention therefore relate to an analysis or synthesis window or a windowing device or method. In addition, an analysis or synthesis filter bank is described, or a method for analyzing or synthesizing a signal using a window. Naturally, a computer program that implements one of the above methods is also disclosed.
[0256] The implementation according to the embodiments of the present invention may be implemented as a hardware implementation, a program implementation or a combination of both. Data, vectors or variables generated, received or otherwise stored for processing can be stored in various types of memory, such as random access memory, buffers, read-only memory, non-volatile memories (eg EEPROMs, flash memories) or other memories such as magnetic or optical memories. The entry position can be, for example, one or more memory units required to store or store relevant amounts of data, such as variables, parameters, vectors, matrices, window coefficients, or other pieces of information and data.
[0257] Program implementations may operate on different computers, computer-type systems, processors, ASIC (application-specific integrated circuit) or other integrated circuits (ICs).
[0258] Depending on certain embodiments of embodiments of the methods of the invention, embodiments of the methods of the invention may be implemented by hardware, software or a combination of both. The implementation can be carried out using a digital storage medium, in particular a CD, DVD or other disk containing an electronically readable control signal stored thereon, which interacts with a programmable computer system, processor or integrated circuit, so that an embodiment of the method of the invention is implemented. In general, an embodiment of the present invention is thus a computer program product with a program code stored on a machine readable carrier such that the program code functions to implement an embodiment of the methods of the invention, when the product being a computer program is running on a computer, processor or integrated circuit. In other words, embodiments of the methods of the invention are, therefore, a computer program having a program code for performing at least one embodiment of the methods of the invention when the computer program is running on a computer, processor or integrated circuit.
[0259] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that the first portion of the analysis window function includes a window coefficient having a maximum absolute value greater than 1.
[0260] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that the analysis window function is characterized by oscillating behavior.
[0261] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that all window coefficient sequence window coefficients are window coefficients with real values.
[0262] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that the frame (120) of the time domain audio sample inputs includes a T block sequence (130) input audio samples in the time domain extending from the earliest to the latest input audio samples in the time domain of the frame (120), each block comprising N input audio samples in the time domain, wherein T and N are positive integers, and T is greater from 4.
[0263] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that windowing comprises a multiplication depending on the input element of the audio samples in the time domain of the frame (120) by window coefficients of window coefficients.
[0264] In an apparatus for generating audio subband values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that each audio time domain input signal is multiplied depending on the element by the window coefficient of the function analysis windows according to the sequence of input audio samples in the time domain and the sequence of window coefficients.
[0265] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that for each of the audio time-domain samples of the frame (120) of the input audio samples in in the time domain, exactly one windowed sample is generated.
[0266] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that the window coefficient corresponding to the coefficient index n = (T-3) · N of the window contains a value less than -0.1, wherein the sequence index of the window coefficients is an integer in the range 0 to N · T - 1, and wherein the window coefficient used for windowing the last audio sample in the time domain is the window coefficient corresponding to the index N · T - 1.
[0267] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that the first portion of the window coefficients comprises 3/2 · N window coefficients and the second part of the coefficients window contains (T-3/2) · N window coefficients of window coefficients sequence.
[0268] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that window coefficients c (n) satisfy the dependencies given in the table in annex 3.
[0269] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that window coefficients c (n) satisfy the relationships given in the table in appendix 2.
[0270] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windshift module (110) is adapted such that window coefficients c (n) satisfy the relationships given in the table in Annex 1.
[0271] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windowing module (110) or device (100) is adapted such that the analysis window function (190) includes the first number of window coefficients acquired from a larger window function containing a sequence of a larger, second number of window coefficients, wherein window coefficients of a window function are acquired by interpolating window coefficients of a larger window function and wherein the second number is an even number.
[0272] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windowing module (110) or device (100) are adapted such that window coefficients of the window function are linearly interpolated.
[0273] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windowing module (110) or device (100) are adapted such that the window coefficients of the analysis window function are interpolated based on two consecutive ones. Window coefficients of a larger window function according to a sequence of window coefficients of a larger window function to obtain a window coefficient of a window function.
[0274] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the analysis windowing module (110) or device (100) are adapted to obtain coefficients c (n) of the analysis window function window based on the equation
<img file="PL2076901T3_D0019.tif" />
where n is an integer indicating the coefficient index c (n) of the window, and c2 (n) is the window coefficient of the larger window function.
[0275] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the device (100) is adapted such that the current frame (120) of the input audio samples in the time domain to be processed is generated by shifting (T-1) the subsequent blocks of the immediately preceding frame (120) of the audio time domain input samples one block towards the earlier input audio samples in the time domain and by adding one block (220) of fresh audio samples in the time domain as a block containing the last input audio samples in the area of the current time frame (120).
[0276] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the device (100) is adapted such that the current frame (120) of the x (n) audio input samples in the time domain to be processed, is generated based on the shift of input xprev (n) audio samples in the time domain of the immediately preceding frame (120) of the input time-domain audio samples based on the equation
<img file="PL2076901T3_D0020.tif" />
for the time or index n = 32, 319 of the sample and wherein the apparatus (100) is further adapted to generate input x (n) audio samples in the time domain of the frame (120) of the time domain audio input samples by capturing 32 subsequent incoming input samples in the time domain according to the order of incoming time-domain audio input samples of decreasing time or n sample indices for the input x (n) audio samples in the time domain of the current frame (120), starting with the time or index n = 31 samples.
[0277] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the calculator (170) includes a time-frequency transducer adapted to generate audio subband values in such a way that all subband values based on one frame (150) windowed samples represent the spectral representation of windowed frame samples (150) of windowed samples.
[0278] In a device for generating audio subbands values in audio subband channels according to embodiments of the present invention, the time-frequency transducer is adapted to generate subband values with complex values.
[0279] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, calculator (170) is adapted to calculate one audio subbands value for each input audio sample in the time domain of one block (130) of audio input inputs in the field the calculation of each value of the audio subbands or each of the input audio samples in the time domain of one block (130) of the input time-domain audio samples is based on the windowed samples of the windowed frame (150).
[0280] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, calculator (170) is adapted to calculate audio subbands values based on multiplication of windowed samples (150) by harmonically oscillating function for each subband value and adding up multiplied windowed samples, wherein the frequency of the harmonically oscillating function is based on the center frequency of the respective subband subband value.
[0281] In a device for generating audio subband values in audio subband channels according to embodiments of the present invention, the calculator (170) is adapted such that the harmonically oscillating function is a combined exponential function, a sine function or a cosine function.
[0282] In a device for generating audio subband values in audio subband channels according to embodiments of the present invention, the calculator (170) is adapted to calculate values for watt audio subbands based on the equation <sup>AT</sup>n = Σ <sup>Ζ</sup>(<sup>Π +</sup> J ' <sup>64</sup>) j = 0 for n = 0, ..., 63 i = £ u "2 fj ·? - (k + 0.5) · (2n - 95) 1 for k = 0,., 31, with z (n ) is a windowed sample corresponding to the index n, where k is the subband index, where 1 is the block index (180) of the audio subbands values and where fosc (x) is an oscillating function dependent on the xo variable real values.
[0283] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the calculator (170) is adapted such that the oscillating function fosc (x) is <sup>f</sup>osc (<sup>X</sup>) = θ<sup>χ</sup>ρ (4 · <sup>X</sup>) or
<img file="PL2076901T3_D0021.tif" />
likes<sub>ABOUT</sub>sc (*) = sin (x) where i is an imaginary unit.
[0284] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, the device (100) is adapted to process a frame (120) of real time audio input audio samples.
[0285] In an apparatus for generating audio subbands values in audio subband channels according to embodiments of the present invention, device (100) is adapted to provide a signal indicating a synthesis window function (370) for use with audio subband values or indicating function (190) of the analysis window; used to generate values of audio subbands.
[0286] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the device (300) is adapted to generate a block (410) of audio samples in the time domain, wherein the block (410) of time-domain audio samples comprises N samples audio in the time domain, where N is a positive integer.
[0287] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the device (300) is adapted to generate a block (410) of time-domain audio samples based on a block (320) of audio subband values including N subband values. and wherein the calculator (310) is adapted to calculate the sequences (330) of intermediate audio samples in the time domain including T · N of the intermediate audio samples in the time domain, wherein T is a positive integer.
[0288] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshift module (360) is adapted such that the synthesis window function is asymmetric with respect to the window coefficient of the sequence.
[0289] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshielding module (360) is adapted such that the first portion comprises a maximum value of all window coefficients of a synthesis window function having an absolute value greater than 1.
[0290] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshielding module (360) is adapted such that the function (370) of the synthesis window is characterized by oscillating behavior.
[0291] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshift module (360) is adapted such that the first portion comprises 3/2 · N window coefficients and the second part of the window coefficients comprises (T -3/2) · N window coefficients, where T is an index greater than or equal to 4, indicating the number of blocks 340 contained in the frame (330) of intermediate time domain samples.
[0292] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshielding module (360) is adapted such that windowing of the intermediate time sample sequences comprises multiplication depending on the intermediate element of the time-domain samples by window coefficient.
[0293] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshift module (360) is adapted such that each intermediate time domain sample is multiplied depending on the element by the window coefficient of the function (370) synthesis windows according to the sequence of intermediate time domain samples and the sequence of window coefficients.
[0294] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshift module (360) is adapted such that the window coefficients of the synthesis window function (370) are real-valued values.
[0295] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshielding module (360) is adapted such that the window coefficient c (n) satisfies the relationships given in the Appendix 3 table.
[0296] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshielding module (360) is adapted such that the coefficients c (n) of the window satisfy the relationship given in the annex 2 table.
[0297] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windshielding module (360) is adapted such that window coefficients c (n) satisfy the relationships given in the Appendix 1 table.
[0298] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windower module (360) or device (300) is adapted such that the synthesis window function comprises a first number of window coefficients derived from a larger window function comprising a sequence of a larger, second number of window coefficients, wherein window coefficients of a window function are obtained by interpolating window coefficients of a larger window function and wherein the second number is even.
[0299] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windower module (360) or device (300) is adapted such that the window coefficients of the synthesis window function (370) are interpolated linearly.
[0300] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windower module (360) or device (300) is adapted such that window coefficients of the synthesis window function (370) are interpolated based on two successive window coefficients of a larger window function according to the sequence of window coefficients of a larger window function to obtain a window coefficient of a window function.
[0301] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the synthesis windower module (360) or device (300) is adapted to obtain coefficients c (n) of the synthesis window function window based on the equation
Φ) = I (c<sub>2</sub>(<sup>2n</sup>) + Φ<sup>2η</sup> +!)) where n is an integer indicating the coefficient index c (n) of the window, and c2 (n) is the window coefficient of the larger window function.
[0302] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) is adapted to calculate intermediate time-domain samples of intermediate time sample sequences based on multiplication of audio subbands by harmonically oscillating functions and adding up the multiplied values of the audio subbands, wherein the frequency of the harmonically oscillating function is based on the center frequency of the respective subband.
[0303] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) is adapted in such a way that the harmonically oscillating function is a combined exponential function, a sine function or a cosine function.
[0304] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) is adapted to calculate intermediate time-domain samples with real values based on subband values with complex values.
[0305] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) is adapted to calculate the intermediate sequences of samples from (i, n) with real-time values based on the equation
<img file="PL2076901T3_D0022.tif" />
for n total in the range 0 to N · T-1, where Re (x) is the real part of the number xo complex values, π = 3,14 ... is a circular number, and fosc (x) is harmonically oscillating function, where f<sub>0S</sub>M = exp (i · <sup>x</sup>) · When the values of the audio subbands provided to the calculator are complex values, where I is an imaginary unit, and where
4SC (<sup>X</sup>) = cos (x) when the values of the audio subbands provided to the calculator (310) are real values.
[0306] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) includes a frequency-time transducer adapted to generate intermediate time sample sequences in a time domain such that audio subbands values provided to the calculator (310) represent a representation spectral sequence of intermediate time domain samples.
[0307] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the frequency-time converter is adapted to generate intermediate time sample sequences in the time domain based on complex subband values.
[0308] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) is adapted to calculate intermediate sequences of samples g (n) in time domain from X (k) audio subbands based on equation v ( n) = v<sub>prev</sub>(n - 2N) for n total in the range of 20N-1 and 2N · <sup>e</sup>4 m <sup>+</sup><sup>(2n</sup> -<sup>(in</sup> for n total in the range 0 and 2N-1 and
<img file="PL2076901T3_D0023.tif" />
g (2N · j + k) = v (4Nj + k)
<img file="PL2076901T3_D0024.tif" />
for a total in the range 0 and 4 I for total k in the range 0 and N-1, where N is an integer indicating the number of audio subbands and the number of audio samples in the time domain where v is a vector with real values, where vprev is with vector vectors real values immediately previous generation of audio samples in the time domain, where i is an imaginary unit, and π is an autorphic number.
[0309] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the calculator (310) is adapted to calculate intermediate sequences of samples g (n) in the time domain from X (k) audio subbands based on the equation <sup>V</sup>M = <sup>V</sup>prev (<sup>n</sup> " <sup>2N</sup>) for n total in the range of 20N-1 and 2N v (n) = £ x (k) * = 0 '32' <sup>SOMETHING</sup>G> z7 <sup>+</sup> ~ for n total in the range of 0 and 20N-1 and g (2W · j + N + k) = v (4Nj + 3N + k) g (2N · j + k) = v (4Nj + k) for total j in the range 0 and 4 and for a total k in the range 0 and N-1, where N is an integer indicating the number of audio subbands and the number of audio samples in the time domain where v is a vector with real values, where vprev is a vector vo real values immediately preceding generating audio samples in the time domain and where π is an automorphic number.
[0310] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the (400) output stage with tab is adapted to process windowed intermediate time-domain samples in a overlapping manner, based on T consecutively delivered blocks (320) values of audio subbands.
[0311] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the output stage (400) of a tab-addition is adapted to provide samples out1 (n) in the time domain, where n is an integer indicating a sample index based on equation
Γ-1 out, (n) = z<sub>(1</sub>- *)<sub>n + Jt N</sub>
Jt = O where zl, n is a windowed interim sample in the time domain corresponding to the n sample index and frame or index 1 sequence in the range 0 to T-1, where 1 = 0 corresponds to the last frame or sequence and smaller values of 1 previously generated frames or sequence.
[0312] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the (400) output stage with tab is adapted to provide out (k) samples in the time domain based on the out (k) = w (nn) equation + k), n = 0 where w is a vector containing windowed intermediate samples in the time domain, ak is an integer indicating an index in the range between 0 and (N-1).
[0313] In an apparatus for generating time-domain audio samples according to embodiments of the present invention, the device (300) is adapted to receive a signal indicative of the analysis window function (190) used to generate values of the audio subbands, or indicating a window function (370). a synthesis that is to be used to generate audio samples in the time domain.
[0314] According to embodiments of the present invention, the encoder (510) includes an apparatus (560) for generating audio subbands values in audio subband channels according to an embodiment of the present invention.
[0315] According to embodiments of the present invention, the encoder (510) further comprises a quantizer and encoder (570) coupled to the device (560) for generating audio subbands values and adapted to quantize and encode the values of the audio subbands output from the device (560) and to output quantized encoded values of audio subbands.
[0316] According to embodiments of the present invention, the decoder (580) comprises a device (600) for generating time-domain audio samples according to an embodiment of the present invention.
[0317] According to embodiments of the present invention, the decoder (580) further comprises a decoder and dequantizer (590) adapted to receive coded and quantized audio subband values coupled to a device (600) for generating time-domain audio samples and adapted to provide decoded and de-quantized values of the audio subbands as the values of the audio subbands to the device (600).
[0318] According to embodiments of the present invention, the SBR encoder (520) comprises an apparatus (530) for generating audio subband values in audio subband channels based on a time domain input audio sample frame supplied to the SBR encoder (520) and the module (540). acquiring SBR parameters coupled to the device (530) for generating audio subband values and adapted to acquire and output SBR parameters based on the values of the audio subbands.
[0319] According to embodiments of the present invention, the system (610) includes a device (620) for generating audio subbands values from a frame of audio time domain input inputs provided to the system (610); and a device (640) for generating time-domain audio samples based on the values of the audio subbands generated by the device (640) for generating audio subband values.
[0320] According to embodiments of the present invention, the arrangement (610) is an SBR decoder.
[0321] According to embodiments of the present invention, the system further comprises a HF generator (630) connected between the device (620) for generating audio subbands values and device (640) for generating time-domain audio samples and adapted to receive SBR data, adapted for modification or adding audio subbands values based on SBR data and audio subband values from the device (620) to generate audio subband values.
[0322] For all devices and methods according to embodiments of the present invention, depending on the details of implementation, to make the window coefficients based on the values given in the tables in appendixes 1 and 3, additional sign changes may be made with respect to the window coefficients corresponding to indexes 128 to 255 and 384 to 511 (multiplication by factor (-1)) can be implemented in accordance with equations (16a) and (16b). In other words, window window function coefficients are based on the window coefficients given in the table in Annex 1. For window coefficients of the window functions shown in the figures, window coefficients in the table corresponding to indexes 0 to 127, 256 to 383 and 512 to 639 must be multiplied ( by (+1) (ie there is no character change), and the window coefficients corresponding to indexes 128 to 255 and 384 to 511 must be multiplied by (-1) (i.e., there is a sign change) to obtain the window coefficients of the window function shown. Correspondingly, the dependences given in the table in annex 3 must be treated accordingly. In other words, the window coefficients given in the tables in appendixes 1 to 4 can be changed in accordance with equations (16a) and (16b).
[0323] It should be noted that within the framework of the present application, the equation based on the equation is understood to include additional delays, factors, additional coefficients and the introduction of another simple function. In addition, simple solid constituents of sums etc. can be omitted. In addition, also include algebraic transformations, equivalence and approximation transformations (eg Taylor approximation) that do not change the result of the equation completely or significantly. In other words, both small modifications and transformations leading to substantially identical in terms of the result are included in the case where the equation or expression is based on an equation or expression.
[0324] The apparatus for generating audio subband values in the audio subband subbands of embodiments of the present invention comprises an analysis windshield 110 module for windowing a frame of time-domain input audio samples 120 extending from an early sample to a subsequent sample using an analysis window function 190 comprising a sequence of window coefficients for obtaining windowed samples. The analysis window function 190 includes a first group of 200 window coefficients comprising a first portion of the window coefficient sequence and a second window window coefficient group 210 comprising a second portion of the window factor sequence. The first part contains fewer window coefficients than the second part. The energy value of the total window coefficients in the first part is higher than the energy value of the total window coefficients of the second part, the first group of window coefficients being used for windowing the later time domain samples, and the second window coefficient group being used for windowing the earlier time domain samples. The apparatus further comprises a calculator 170 for calculating the values of the audio subbands using the windowed samples, wherein the calculator 170 comprises a time-frequency transducer adapted to generate values of the audio subbands in such a way,
[0325] In such an apparatus for generating 100 complex audio subband values according to an embodiment of the present invention, the analysis windowing module 110 may be adapted such that the window coefficient corresponding to the index n = (T-1) · N contains an absolute value in in the range 0.9 to 1.1, wherein the sequence index of the window coefficients is an integer in the range 0 to N · T-1, wherein the window coefficient used for windowing the last input audio sample in the time domain of the frame 120 is the window coefficient corresponding to the index N · T-1, wherein the analysis windowing module 110 is adapted in such a way,that a frame 120 of time-domain audio samples comprises a T-sequence of audio time input sample input blocks 130 extending from the earliest to last input audio samples in the time domain of frame 120, each block comprising N audio input inputs in the time domain, and taking T and N are positive integers and T is greater than 4. In a device for generating 100 complex audio subband values according to such an embodiment of the present invention, the analysis windower 110 can additionally be adapted such that a window coefficient corresponding to the index of coefficients n = N · T-1 of the window contains an absolute value less than 0.02.and wherein T and N are positive integers and T is greater than 4. In a device for generating 100 complex audio subband values according to an embodiment of the present invention, the analysis windowing module 110 can be further adapted such that the coefficient windows corresponding to the index of coefficients n = N · T-1 of the window contain an absolute value less than 0.02.and wherein T and N are positive integers and T is greater than 4. In a device for generating 100 complex audio subband values according to an embodiment of the present invention, the analysis windowing module 110 can be further adapted such that the coefficient windows corresponding to the index of coefficients n = N · T-1 of the window contain an absolute value less than 0.02.
[0326] In an apparatus for generating 100 complex audio subband values according to an embodiment of the present invention, the analysis windowing module 110 may be adapted such that windowing includes multiplication of the input x (n) audio samples in the time domain of the frame 120 for obtaining a windowed samples from (n) windowed frame based on the equation
<img file="PL2076901T3_D0025.tif" />
where n is an integer indicating the sequence index of window coefficients in the range 0 to T · N-1, where c (n) is the window coefficient of the analysis window function corresponding to index n, where x (N · T-1) is the last input audio sample in the time frame of the input audio sample frame 120, wherein the analysis windowing module 110 is adapted such that the input time frame 120 of the audio time samples comprises a sequence T of audio sample input blocks 130 in a time domain extending from the earliest to the latest input samples frame-by-frame audio 120, each block comprising N input audio samples in the time domain and wherein T and N are positive integers and T is greater than 4.In the apparatus 100 for generating values of audio subbands of complex values according to such an embodiment of the present invention, the analysis windower module 110 can additionally be adapted in such a way that the coefficients c (n) of the window satisfy the relationships given in the table in annex 4.
[0327] In an apparatus for generating 100 complex audio subband values according to an embodiment of the present invention, the device 100 may be adapted to use the 190 time window analysis function or the index-reversed version of the synthesis window function 370 to be used. for values of audio subbands.
The frequency / time converter is adapted to generate intermediate sequences of time-domain samples based on the values of complex audio subbands. The apparatus for generating real-time audio samples 300 in accordance with an embodiment of the present invention further comprises a 360 windowing module for windowing the intermediate time sample sequence 330 using a synthesis window function 370 comprising a window coefficient sequence for obtaining windowed intermediate samples in the field time, wherein the synthesis window function 370 comprises a first window window coefficient group 420 comprising a first portion of the window coefficient sequence and a second window window coefficient group 430 comprising a second portion of the window factor sequence, the first part has fewer window coefficients than the second part. The energy value of the total window coefficients in the first part is higher than the energy values of the total window coefficients of the second part, the first group of window coefficients being used for windowing the later intermediate time domain samples, and the second window coefficient group being used for windowing the previous intermediate samples in the field time. The apparatus 300 additionally includes an outbound 400 stage with a tab for processing windowed intermediate time samples to obtain time domain samples. wherein the first group of window coefficients is used for windowing the later intermediate time domain samples, and the second group of window coefficients is used for windowing the earlier intermediate time domain samples. The apparatus 300 additionally includes an outbound 400 stage with a tab for processing windowed intermediate time samples to obtain time domain samples. wherein the first group of window coefficients is used for windowing the later intermediate time domain samples, and the second group of window coefficients is used for windowing the earlier intermediate time domain samples. The apparatus 300 additionally includes an outbound 400 stage with a tab for processing windowed intermediate time samples to obtain time domain samples.
[0329] In a real time audio data generation device 300 according to an embodiment of the present invention, the window coefficient corresponding to the index n = N can include an absolute value in the range between 0.9 and
The index n of the window coefficient sequence is an integer in the range 0 to T · N-1, wherein the window coefficient used for windowing the last intermediate time-domain sample is the window coefficient corresponding to the index n = 0, wherein T is an integer greater than 4, indicating the number of blocks contained in frame 330 intermediate time domain samples, wherein the device 300 may be adapted to generate a block of 410 audio samples in the time domain, wherein the time domain block 410 comprises N audio samples in time domain, wherein N is a positive integer. In a device for generating samples 300 audio with real values in the time domain according to such an embodiment, the synthesis windowing module 360 may additionally be adapted in such a way,
[0330] In a 300 audio real time sample generator according to an embodiment of the present invention, the synthesis windshift module 360 may be adapted such that the window coefficient corresponding to the index n = 3N is less than -0.1, with wherein the apparatus 300 may further be adapted to generate a block of 410 audio samples in the time domain, wherein the time domain block 410 of the audio samples includes N audio samples in the time domain, wherein N is a positive integer.
[0331] In a real-time domain audio sampling device 300 according to an embodiment of the present invention, the synthesis windshift module 360 may be adapted such that the windowing includes multiplication of intermediate samples g (n) in the time domain of the intermediate sample sequences in time domain for obtaining windowed samples from (n) windowed frame (380) based on the equation ζ (η) = g (n) · c (T · Ν - 1 - η) for n = 0, ..., T · N - 1. In an apparatus for generating samples 300 of real-time values in accordance with such an embodiment of the present invention, the synthesis windowing module 360 may additionally be adapted in such a way that the window coefficient c (n) satisfies the relationships given in the table in the annex. 4.
<td>Annex 1</td><td></td><td>· -</td><td>and [35]</td><td>=</td><td>5.764734796907189e-001</td>
<td></td><td></td><td></td><td>and [36]</td><td>=</td><td>5.930981800982896e-001</td>
<td>a [0]</td><td>=</td><td>1.129580193872797e-002</td><td>in [37]</td><td>=</td><td>6.096690552916387e-001</td>
<td>in [l]</td><td>=</td><td>2.353059744 904218e-002</td><td>and [38]</td><td>=</td><td>6.261725236758639e-001</td>
<td>in [2]</td><td>=</td><td>3.45071874872125le-002</td><td>and [39]</td><td>=</td><td>6.425939632009995e-001</td>
<td>in [3]</td><td>=</td><td>4.634695977000525e-002</td><td>and [40]</td><td>=</td><td>6.589148753746076e-001</td>
<td>in {4]</td><td>=</td><td>5.918677345174197e-002</td><td>and [41]</td><td>=</td><td>6.751199626157149e-001</td>
<td>and [5]</td><td>=</td><td>7.325978412117062e-002</td><td>and [42]</td><td>=</td><td>6.911981575264606e-001</td>
<td>in [6]</td><td>=</td><td>8.829745229234007e-002</td><td>and [43]</td><td>=</td><td>7.071447728928043e-001</td>
<td>in [7]</td><td>=</td><td>1.042033024802571e-001</td><td>in [4 4]</td><td>=</td><td>7.229599104052475e-001</td>
<td>in [8]</td><td>=</td><td>1.206924277410051e-001</td><td>and [45]</td><td>=</td><td>7.386515025302785e-001</td>
<td>in [9]</td><td>=</td><td>1.376149808913910e-001</td><td>and [46]</td><td>=</td><td>7.542294504292890e-001</td>
<td>and [10]</td><td>=</td><td>1.547461142258783e-001</td><td>and [47]</td><td>=</td><td>7.697093346240386e-001</td>
<td>in [ll]</td><td>=</td><td>1.719726384566089e-001</td><td>and [48]</td><td>=</td><td>7.851012620144958e-001</td>
<td>and [12]</td><td>=</td><td>1.891590407342011e-001.</td><td>and [49]</td><td>=</td><td>8.004165237845137e-001</td>
<td>in [13]</td><td>'=</td><td>2.062605107774960e-001</td><td>and [50]</td><td>=</td><td>8.156523162880560e-001</td>
<td>and [14]</td><td>=</td><td>2.232276864673650e-001</td><td>and [51]</td><td>=</td><td>8.308039608112368e-001</td>
<td>and [15]</td><td>=</td><td>2.400768261284114e-001</td><td>and [52]</td><td>=.</td><td>8.458450064727010e-001</td>
<td>and [16]</td><td>=</td><td>2.568176309566753e-001</td><td>and [53]</td><td>=</td><td>8.607492455327098e-001</td>
<td>and [17]</td><td>=</td><td>2.734977190313227e-001</td><td>and [54]</td><td>=</td><td>8.754640719350776e-001</td>
<td>in [18]</td><td>=</td><td>2.901491317310591e-001</td><td>and [55]</td><td>=</td><td>8.899474405744183e-001</td>
<td>and [19]</td><td>=</td><td>3.068186515423912e-001</td><td>and [56]</td><td>=</td><td>9.041286138017367e-001</td>
<td>and [20]</td><td>=</td><td>3.235298682841570e-001</td><td>and [57]</td><td>=</td><td>9.179666107725365e-001</td>
<td>and [21]</td><td>=</td><td>3.403074146062977e-001</td><td>and [58]</td><td>=</td><td>9.313874086278087e-001</td>
<td>and [22]</td><td>=</td><td>3.571527896130669e-001.</td><td>and [59]</td><td>=</td><td>9.443802853939540e-001</td>
<td>and [23]</td><td>=</td><td>3.74<sub>;</sub>0643974275026e-001</td><td>and [60]</td><td>=</td><td>9.568885413848645e-001</td>
<td>and [24]</td><td>=</td><td>3.910243970160607e-001</td><td>and [61]</td><td>=</td><td>9.690016637782843e-001</td>
<td>and [25]</td><td>=</td><td>4.080154903861317e-001</td><td>and [62]</td><td>=</td><td>9.807691702375303e-001</td>
<td>and [26]</td><td>=</td><td>4.250144186334534e-001</td><td>and [63]</td><td>=</td><td>9.927543720639498e-001</td>
<td>and [27]</td><td>=</td><td>4.420013942269341e-001</td><td>and [64]</td><td>= </td><td>1.001463112557766e +000</td>
<td>and [28]</td><td>=</td><td>4.589582896478246e-001</td><td>and [65]</td><td>=</td><td>1.006893331637123e +000</td>
<td>and [29]</td><td>=</td><td>4.758753745532750e-001</td><td>and [66]</td><td>=</td><td>1.012508393574432e +000</td>
<td>and [30]</td><td>=</td><td>4.927463828072591e-001</td><td>and [67]</td><td>=</td><td>1.017729040219375e +000</td>
<td>and [31]</td><td>=</td><td>5.095720854151864e-001</td><td>and [68]</td><td>=</td><td>1.022470190536100e +000</td>
<td>and [32]</td><td>=</td><td>5.263554446856779e-001</td><td>and [69]</td><td>=</td><td>1.026615653698808e +000</td>
<td>and [33]</td><td>=</td><td>5.430990601899994e-001</td><td>and [70]</td><td>=</td><td>1.030198648769593e +000</td>
<td>and [34]</td><td>=</td><td>5.598052330684253e-001</td><td>. and [71]</td><td>=</td><td>1.033205850580933e +000</td>
in [72] = 1.035694432087486e + 000 in [73J = 1.037 6B316529758-6e + 000 in [74] = 1.039227995800217e + 000 in [75] = 1.040349586463588e + 000 in [76] = 1.041086497214721e + 000 in (77) = 1.041443375950143e + 000 in [78] = 1.041434355650865e + 000 in [79j = 1.04104 318 4 21617 le-i-000 in [80] = 1.040262316588456e + 000 in [81] = 1.039061496136853e + 000 in [82J = 1.037422300157921 e + 000 in [83] = 1.0353U720204252e + 000 in [84] = 1.032712952177121e + 000 in [85] = 1.029600494883906e + 000 in [86] = 1.025966756910904e + 000 in [87] = 1.021798805583990e + 000 in [ 88] = 1.017100128250049e + 000 in [89] = 1.011867706519706e + 000 in [90] = 1.006109248754940e + 000 in [91] = 9.998285752401580e-001 in [92] = 9.930379854679836e-001 in [93] = 9.857387823493258e -001 in [94] = 9.779405164766706e-001 in [95] = 9.696426101291272e-001 in [96] = 9.6085195161401501-001 in [97] = 9.515674613550604e-001 in [98] = 9.417975696327747e-001 in [99 ] = 9.315442093447622e-001 in [100] = 9.208194746232827e-001 in [101] = 9.096310803629866e-001 in [102] = 8.979959173503500e-001 in [103] = 8.859232320517536e-001 in [104] = 8.734366852542127e-001 in [ 105] = 8.605542791988831e-001 w't.106] = 8.472 98714 5504 696e-001 in [107] = 8.336863467961255e-001 in [108] = 8.197387292306723e-001 in [109] = 8.054701312929008e-001 in (110 ] = 7.908995350037713e-001 in [III] = 7.760385598209244e-001 in [112] = 7.609051036128973e-001 in [113] = 7.455111681431031e-001 in [U4] = 7.298745530879272e-001 in [115] = 7.140087729493950e- 001 in [116] = 6.979336851549095e-001 wii! 7j = 6.816667882498023e-O01 in [118] = 6-652304141388827e-001 in [119] = 6.486437667370537e-001 in [120] = 6.319284031798550e-001 in (121) = 6.151031151692835e-001 in [122] = 5.981877665956570e-001 in [123] = 5.8Γ1992722116214e-001 in [124] = 5.641522833259215e-001 in [125] = 5.470652177576862e-001 in [126] = 5.299509559653194e-001 in [127] = 5.128557121424191e-001 in [128] = -4.956175421414453e-001 in [129] = -4.782650346610896e-001 in [130] = -4.609828932783459- 001 in [131] = -4.437530233023859e-001 in [132] = -4.265950246465440e-001 in [133] = -4.095160467543179e-001 in [134] = -3.925409172155113β-00ϊ in [135] = -3.756821671788237e- 001 in [136] = -3.589626517817934e-001 in [137] = -3.423942311297658e-001 in [138] = -3.259993851088293e-001 in [139] = -3.097861805973821e-001 in [140] = -2.937724988593393e- 001 in [141] = -2.779637821990255e-001 in [142] = -2.62374915948804le-001 in [143] = -2.470098299603623e-001 in [144] = -2.318815478758375e-001 in [145] = -2.169925682529340e- 001 in [146] = -2.023548005388463e-001 in [147] = -1.879711746686855e-001782650346610896e-001 in [130] = -4.609828932783459e-001 in [131] = -4.437530233023859e-001 in [132] = -4.265950246465440e-001 in [133] = -4.095160467543179e-001 in [134] = -3.925409172155113 β-00ϊ in [135] = -3.756821671788237e-001 in [136] = -3.589626517817934e-001 in [137] = -3.423942311297658e-001 in [138] = -3.259993851088293e-001 in [139] = -3.097861805973821 e-001 in [140] = -2.937724988593393e-001 in [141] = -2.779637821990255e-001 in [142] = -2.62374915948804le-001 in [143] = -2.470098299603623e-001 in [144] = -2.318815478758375 e-001 in [145] = -2.169925682529340e-001 in [146] = -2.023548005388463e-001 in [147] = -1.879711746686855e-001782650346610896e-001 in [130] = -4.609828932783459e-001 in [131] = -4.437530233023859e-001 in [132] = -4.265950246465440e-001 in [133] = -4.095160467543179e-001 in [134] = -3.925409172155113 β-00ϊ in [135] = -3.756821671788237e-001 in [136] = -3.589626517817934e-001 in [137] = -3.423942311297658e-001 in [138] = -3.259993851088293e-001 in [139] = -3.097861805973821 e-001 in [140] = -2.937724988593393e-001 in [141] = -2.779637821990255e-001 in [142] = -2.62374915948804le-001 in [143] = -2.470098299603623e-001 in [144] = -2.318815478758375 e-001 in [145] = -2.169925682529340e-001 in [146] = -2.023548005388463e-001 in [147] = -1.879711746686855e-001589626517817934e-001 in [137] = -3.423942311297658e-001 in [138] = -3.259993851088293e-001 in [139] = -3.097861805973821e-001 in [140] = -2.937724988593393e-001 in [141] = -2.779637821990255 e-001 in [142] = -2.62374915948804le-001 in [143] = -2.470098299603623e-001 in [144] = -2.318815478758375e-001 in [145] = -2.169925682529340e-001 in [146] = -2.023548005388463 e-001 in [147] = -1.879711746686855e-001589626517817934e-001 in [137] = -3.423942311297658e-001 in [138] = -3.259993851088293e-001 in [139] = -3.097861805973821e-001 in [140] = -2.937724988593393e-001 in [141] = -2.779637821990255 e-001 in [142] = -2.62374915948804le-001 in [143] = -2.470098299603623e-001 in [144] = -2.318815478758375e-001 in [145] = -2.169925682529340e-001 in [146] = -2.023548005388463 e-001 in [147] = -1.879711746686855e-001
<td>and [148]</td><td>= -1. 738542127021508e-001</td><td>and [186]</td><td>=</td><td>1.238868653862843e-001</td>
<td>wll49]</td><td>= -1.600061812-296078e-001</td><td>and [187]</td><td>=</td><td>1.251477258491527e-001</td>
<td>and [150]</td><td>= -1.464389150679625e-001</td><td>and [188]</td><td>=</td><td>1.261262023246478e-001</td>
<td>and [151]</td><td>= -1.331544923127771e-001</td><td>and [189]</td><td>=</td><td>1.268280540744526e-001</td>
<td>and [152]</td><td>= -1.201628679722633e-001</td><td>and [190]</td><td>=</td><td>1.272498700590511e-001</td>
<td>and [153]</td><td>= -1.074630704470568e-001</td><td>and [191]</td><td>=</td><td>1.273590703506806e-001</td>
<td>and [154]</td><td>= -9.50696695963251le-002</td><td>and [192]</td><td>=</td><td>1.2745675954 65545e-001</td>
<td>..fi CCI In li JJJ</td><td>_ Λ η Λ <11 Λ -i 1 AA Ί Π Π Ί Λ 1 - Λ Λ η - -0. Z.201U J1U4</td><td>and [193]</td><td>=</td><td>1.275561350483646e-0ul</td>
<td>and [156]</td><td>= -7.120356992726613e-002</td><td>and [194]</td><td>=</td><td>1.273648326872248e-001</td>
<td>and [157]</td><td>= -5.973741829536090e-002</td><td>and [195J</td><td>=</td><td>1.269415772180714e-001</td>
<td>and [158]</td><td>= -4.859005767016811e-002</td><td>and [196]</td><td>=</td><td>1.26299564634067le-001</td>
<td>and [159]</td><td>= -3.775928110298274e-002</td><td>. and [197]</td><td>=</td><td>1.254605188749804e-001</td>
<td>and [160]</td><td>= -2.726484300186575Θ-002</td><td>and [198]</td><td>=</td><td>1.244269583009826e-001</td>
<td>and [161]</td><td>= -1.711323992709580e-002</td><td>and [199]</td><td>=</td><td>1.232131583108813e-001</td>
<td>and [162]</td><td>= -7.298197371320593e-003</td><td>and [200]</td><td>=</td><td>1.218183974842866e-001</td>
<td>and [163]</td><td>= 2.184256929356781e-003</td><td>and [201]</td><td>=</td><td>1.202545652840080e-001</td>
<td>in [164]</td><td>= 1.132324047372148e-002</td><td>and [202]</td><td>=</td><td>1.185243106889108e-001</td>
<td>and [165]</td><td>= 2.012236990754980e-002</td><td>and [203]</td><td>=</td><td>1.166399102636992e-001</td>
<td>and [166]</td><td>= 2.857528272530154e-002</td><td>and [204j</td><td>=</td><td>1.146042249339280e-001</td>
<td>w (167]</td><td>= 3.666942822678171e-002</td><td>and [205]</td><td>=</td><td>1.124296184976912e-001</td>
<td>and [168]</td><td>= 4.4 3 9 6 8 397 8 04 4157 e-0 02</td><td>and [206]</td><td>=</td><td>1.101215600923314e-001</td>
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<td>.. r λ "ii WIOU / J</td><td>=</td><td>-3.460362845825662e-003</td><td>and [345j</td><td>=</td><td>1.0 92 52 614 939127 3e-004</td>
<td>and [308]</td><td>=</td><td>-3.794425324215804e-003</td><td>in [34 6]</td><td>=</td><td>6.415402443848103e-004</td>
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<td>and [310]</td><td>=</td><td>-4.369553676668050e-003</td><td>and [348]</td><td>=</td><td>1.557112059887280e-003</td>
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<td>and [333]</td><td>=</td><td>4.749931197951235e-004</td><td>and [371]</td><td>=</td><td>-9.726698841994444e-004</td>
<td>in [334]</td><td>=</td><td>5.970696819774243e-004</td><td>and [372]</td><td>=</td><td>-1.196637962311630e-003</td>
<td>and [335]</td><td>=</td><td>6.673250213055329e-004</td><td>and [373]</td><td>=</td><td>-1.292865844760059e-003</td>
<td>and [336]</td><td>=</td><td>6.887783835812338e-004</td><td>and [374]</td><td>=</td><td>-1.146268465739874e-003</td>
<td>and [337]</td><td>=</td><td>6.766320515830324e-004</td><td>and [375]</td><td>=</td><td>-1.04059805507447le-003</td>
<td>in [376] = -9.767709065548874e-004</td><td>and [414]</td><td>= -1.815837353167847e-004</td>
<td>in [377] = -9.294665200453614e-0Ó4</td><td>and [415]</td><td>= -3.595054179561440e-004</td>
<td>in [378] = -9.862027119530482e-004</td><td>and [416]</td><td>= -5.901617707607606e-007</td>
<td>in [379] = -1.047654674829846e-003</td><td>and [417]</td><td>= 1.831121301698088e-004</td>
<td>in [380] = -1.099000599887377e-003</td><td>and [418]</td><td>= 9.755685190624611e-005</td>
<td>in [381] = -1.151795860160292e-003</td><td>in (419J</td><td>= 6.606461762989423e-005</td>
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<td>in [383] = -1.250742797799558e-QQ3</td><td>uf 2191 1</td><td>= 4.150075391929448e-005</td>
<td></td><td>"L *" - and</td><td></td>
<td>in [384] = 1.287819050086379e-003</td><td>and [422]</td><td>= 5.021905476506264e-005</td>
<td>in [385] = 1.263569296641556e-003</td><td>and [423]</td><td>= 5.861800137434713e-005</td>
<td>in [386] = 1.226113111394085e-003</td><td>-w [424]</td><td>= 2.126364641291926e-005</td>
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<td>in [388] = 1.122503050159859e-003</td><td>and [426]</td><td>= 9.99O757789944374e-OO5</td>
<td>in [3891 = 1.089428846944533e-003</td><td>and [427]</td><td>= 1.035782617124906e-004</td>
<td>in [390] = 1.O54963366189962e-003</td><td>and [428]</td><td>= 8.870181845310037e-005</td>
<td>in [391] = 9.019128558297515e-004</td><td>and [429]</td><td>= 5.533953373249822e-005</td>
<td>in [392] = 7.847839620863715e-004</td><td>and [430]</td><td>= 1.580188994455254e-005</td>
<td>in [393] = 6.205675927856794e-004</td><td>and [431]</td><td>= 1.277184430250593e-006</td>
<td>in [394] = 3.157663628445906e-004</td><td>and [432]</td><td>= 5.009913312943629e-006</td>
<td>in [395] = 2.556449844935384e-004</td><td>and [433]</td><td>= 1.499170392246774e-005</td>
<td>in [396] = 2.520606580606257e-004</td><td>and [434]</td><td>= 2.241545750231630e-005</td>
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<td>in [401] = 6.193369904730005ę-005</td><td>and [439]</td><td>= 5.408154543124121e-005</td>
<td>in [402] = 3.568554800150508e-005</td><td>and [440]</td><td>= 4.493916063285122e-005</td>
<td>in [403] = 2.443161189273522e-005</td><td>and [441]</td><td>= 2.806963579578946e-005</td>
<td>in [404] = 1.334090914042349e-005</td><td>and [442]</td><td>= 2.364518513682831e-005</td>
<td>in [405] = 2.853437194757816e-006</td><td>and [443]</td><td>= 1.260639764582286e-005</td>
<td>in [406] = -1.039263591111469e-004</td><td>in [4 44]</td><td>= -2.599467772603631e-008</td>
<td>in [407] = 5.144969377044875e-005</td><td>and [445]</td><td>= -1.774108392496017e-005</td>
<td>in [408] = 9.711681816385056e-005</td><td>and [446]</td><td>= -5.889276659458115e-006</td>
<td>in [409] = 2.472023910553232e-005</td><td>and [447]</td><td>= -4.663777919108619e-005</td>
<td>in [410] = 5.397064424090302e-005</td><td>and [448]</td><td>= -2.078886359425321e-004</td>
<td>in [411] = 6.487880719449901e-005</td><td>and [449]</td><td>= -2.131405580107761e-004</td>
<td>in [412] = -5.192444140699947e-005</td><td>and [450]</td><td>= -1.784192600231068e-004</td>
<td>w (413] = -9.204876089551197e-005</td><td>and [451]</td><td>= -1.744841754193053e-004</td>
<td>and [452]</td><td>= -1.728672507238372e-004</td><td>and [490]</td><td>=</td><td>4.</td>
<td>and [453]</td><td>= · -1.885286127508226e-004 -</td><td>and [49l]</td><td>=</td><td>5.</td>
<td>and [454]</td><td>= -2.078299015661617e-004</td><td>and [492]</td><td>=</td><td>4.</td>
<td>and [455]</td><td>= -2.123671573189573e-004</td><td>and [493]</td><td>=</td><td>2.</td>
<td>and [456]</td><td>= -2.415166002501312e-004</td><td>and [494]</td><td>=</td><td>4.</td>
<td>and [457]</td><td>= -2.217025456251449e-004</td><td>and [495]</td><td>=</td><td>3.</td>
<td>and [458]</td><td>= -9.907630821710970e-005</td><td>in [4 96]</td><td>=</td><td>1.</td>
<td>. . r Λ C Λ 1</td><td>_ η nn η o η ί jonrftftiic-.</td><td>. . Γ 4 ΛΤ1</td><td></td><td>ABOUT</td>
<td>In 1 J</td><td>= -0.UJ? Z31401 / 0004JC-UUJ</td><td>WL 4 / J</td><td></td><td>□.</td>
<td>in [460]</td><td>= -7.934509417722400e-005</td><td>and [498)</td><td>=</td><td>7.</td>
<td>and [461]</td><td>= -5.874199358780108e-005</td><td>and [499]</td><td>=</td><td>1.</td>
<td>in [462]</td><td>= -5.449816072329412e-005</td><td>and [500]</td><td>=</td><td>8.</td>
<td>in [463]</td><td>= -4.489491034408147e-005</td><td>and [501]</td><td>=</td><td>8.</td>
<td>in [464]</td><td>= -3.498285982359981e-005</td><td>and [502]</td><td>=</td><td>2.</td>
<td>and [465]</td><td>= -1.748284921486958e-005</td><td>and [503]</td><td>=</td><td>2.</td>
<td>and [466]</td><td>= -9.075430772832575e-006</td><td>and [504]</td><td>=</td><td>1.</td>
<td>and [467]</td><td>= -1.052707430241351e-005</td><td>and [505]</td><td>=</td><td>5.</td>
<td>and [468]</td><td>= -6.538878366985722e-006</td><td>and [506]</td><td>=</td><td>1.</td>
<td>in [4 69]</td><td>= 2.206341308073472e-005</td><td>and [507]</td><td>=</td><td>1.</td>
<td>and [470]</td><td>= 1.769261935287328e-004</td><td>and [508]</td><td>=</td><td>7.</td>
<td>and [471]</td><td>= 6.418658561385058e-005</td><td>and [509]</td><td>=</td><td>4.</td>
<td>in [472]</td><td>= -8.882305312548962e-005</td><td>and [510]</td><td>=</td><td>-1</td>
<td>and [473]</td><td>= -1.721347222211949e-005</td><td>and [511]</td><td>=</td><td>-8</td>
<td>and [474]</td><td>= -6.093372716385583e-005</td><td>and [512]</td><td>=</td><td>-3</td>
<td>and [475]</td><td>= -7.679955330373515e-005</td><td>and [513]</td><td>=</td><td>-4</td>
<td>and [476]</td><td>= 7.194151087015007e-005</td><td>and [514]</td><td>=</td><td>-3</td>
<td>and [477]</td><td>= 7.245095937243279a-005</td><td>and [515]</td><td>=</td><td>-2</td>
<td>and [478]</td><td>= 7.870354371072524e-005</td><td>and [516]</td><td>=</td><td>-2</td>
<td>and [479]</td><td>= 5 - 822201682995846e-004</td><td>and [517]</td><td>=</td><td>-1</td>
<td>and [480]</td><td>= 2.666444630171025e-004</td><td>and [518]</td><td>=</td><td>-6</td>
<td>and [481]</td><td>= 7.872592352725688e-005</td><td>and [519]</td><td>=</td><td>4.</td>
<td>and [482]</td><td>= 7.095886893185526e-005</td><td>and [520]</td><td>=</td><td>1.</td>
<td>and [483]</td><td>= 5.643103068471008e-005</td><td>and [521]</td><td>=</td><td>1.</td>
<td>and [484]</td><td>= 6.904415362098980e-005</td><td>and [522]</td><td>=</td><td>-2</td>
<td>and [485]</td><td>= 4.694251739991356e-005</td><td>and [523]</td><td>=</td><td>-1</td>
<td>and [486]</td><td>= 3.367998338617662e-005</td><td>and [524]</td><td>=</td><td>-1</td>
<td>and [487]</td><td>= 6.481921021601837e-005</td><td>and [525]</td><td>=</td><td>-1</td>
<td>and [488]</td><td>= 6.582328030188790e-005</td><td>and [526)</td><td>=</td><td>-9</td>
<td>and [489]</td><td>= -4.256442530773449e-005</td><td>and [527]</td><td>=</td><td>-4</td>
939392400898679e-005 272982009116034e-005 005269212731273e-005 461876679726978e-005 469729032194765e-006 798519731621893e-007 374896222030490e-006 c _ λ / ί r ·
3DJODJOUJJUUZije "UUO
300588863934780e-006 16889447477006le-005 563819899447630e-006 975977837330335e-006 800455533708622e-005 015445311139832e-005 125134651175812e-005 869707265615299e-006 013259758329981e-005 088325131492173e-005 167101260771279e-006 840577540089826ę-006 .469933448634890e-005. 010079089953001e-006, 299004046633323e-005. 373302115187172e-005. 177468256997963e-005. 976824036182567e-005 .464228015326852e-005 .606050838620834e-005 .261944255489322e-006, 591009581217994e-007. 395220723090848e-005 622786214398703e-005 .043464113212971e-006 .653463907257247e-006. 551250801467300e-008 .907927361317977e-006 .607068622268791e-007 .63610536451001le-007 at [528] = -2.765649762593200e-007 at [529J = -1.922074581855119e-006 at [530] = -9.897194091136331e-007 at [531] = - 7.873304717454037e-008 in [532] = 2.945239208477290e-008 at (533] = -2.08 in [633] = -5.426597100684762e-009 in [634J = 4.292861814894369e-007 in [635) = 6.834209542421138e-007 in [636] = 7.099633014995863e-007 in [637] = 8.109951846981774e-007 in [638] = 4.118359768898598e-007 in [639] = 6.571760029213382e-007
<td>iex 2</td><td></td><td>/</td><td>1 in [36]</td><td>1</td><td>= 5.930981800982896e-001</td>
<td></td><td></td><td>1</td><td>1 in [37]</td><td></td><td>= 6.096690552916387e-001</td>
<td>a [0]</td><td>1</td><td>= 1.129580193872797e-002</td><td>1 in [38]</td><td>1</td><td>= 6.261725236758639e-001</td>
<td>in [l]</td><td>1</td><td>= 2.353059744904218e-002</td><td>1 in [39]</td><td>1</td><td>= 6.425939632009995e-001</td>
<td>in [2]</td><td>1</td><td>= 3.450718748721251e-002</td><td>And in [40]</td><td>1</td><td>= 6.5B9148753746076e-001</td>
<td>in [3]</td><td>1</td><td>= 4.634695977000525e-002</td><td>1 in [41]</td><td>1</td><td>= 6.751199626157149e-001</td>
<td>in [4]</td><td>1</td><td>= 5.918677345174197e-002</td><td>1 in [42]</td><td>1</td><td>= 6.911981575264606e-001</td>
<td>and [5]</td><td>and</td><td>= 7.325978412117062e-0Ó2</td><td>1 in [43]</td><td>1</td><td>= 7.071447728928043e-001</td>
<td>in [6]</td><td>1</td><td>= 8.829745229234007e-002</td><td>| and [44]</td><td>1</td><td>= 7.229599104052475e-001</td>
<td>in [7]</td><td>1</td><td>= 1.042033024802571e-001</td><td>And in [45]</td><td>1</td><td>= 7.386515025302785e-001</td>
<td>in [8]</td><td>1</td><td>= 1.206924277410051e-001</td><td>1 in [46]</td><td>1</td><td>= 7.542294504292890e-001</td>
<td>in [9]</td><td>1</td><td>= 1.37614980891391Oe-001</td><td>1 in [47]</td><td>1</td><td>= 7.697093346240386e-001</td>
<td>and [10]</td><td>1</td><td>= 1.547461142258783e-001</td><td>| and [48]</td><td>1</td><td>= 7.851012620144958e-001</td>
<td>in [ll]</td><td>1</td><td>= 1.719726384566089e-001</td><td>1 in [49]</td><td>1</td><td>= 8.004165237845137e-001</td>
<td>and [12]</td><td>1</td><td>= 1.891590407342011e-001</td><td>1 in [50]</td><td>1</td><td>= 8.156523162880560e-001</td>
<td>and [13]</td><td>1</td><td>= 2.062605107774960e-001</td><td>1 in [51]</td><td>1</td><td>= 8.308039608112368e-001</td>
<td>and [14]</td><td>1</td><td>= 2.232276864673650e-001</td><td>1 in [52]</td><td>1</td><td>= 8.458450064727010e-001</td>
<td>and [15]</td><td>1</td><td>= 2.400768261284114e-001</td><td>1 in [53]</td><td>1</td><td>= 8.607492455327098e-001</td>
<td>in (16]</td><td>1</td><td>= 2.568176309566753e-001</td><td>1 in [54]</td><td>1</td><td>= 8.754640719350776e-001</td>
<td>and [17]</td><td>1</td><td>= 2.734977190313227e-001</td><td>1 in [55]</td><td>1</td><td>= 8.899474405744183e-001</td>
<td>and [18]</td><td>1</td><td>= 2.901491317310591e-001</td><td>1 in [56]</td><td>1</td><td>= 9.041286138017367e-001</td>
<td>and [19]</td><td></td><td>= 3.068186515423912e-001</td><td>1 in [57]</td><td>1</td><td>= 9.179666107725365e-001</td>
<td>and [20]</td><td>1</td><td>= 3.235298682841570e-001</td><td>1 in [58]</td><td>1</td><td>= 9.313874086278087e-001</td>
<td>and [21]</td><td>1</td><td>= 3.403074146062977e-001</td><td>1 in [59]</td><td>1</td><td>= 9.443802853939540e-001</td>
<td>in (22]</td><td>1</td><td>= 3.571527896130669e-001</td><td>1 in [60]</td><td>1</td><td>= 9.568885413848645e-001</td>
<td>and [23]</td><td>1</td><td>= 3.740643974275026e-001</td><td>1 in [61]</td><td>1</td><td>= 9.690016637782843e-001</td>
<td>and [24]</td><td>1</td><td>= 3.910243970160607e-001</td><td>1 in [62]</td><td>1</td><td>= 9.807691702375303e-001</td>
<td>and [25]</td><td>1</td><td>= 4.080154903861317e-001</td><td>1 in [63]</td><td>1</td><td>= 9.927543720639498e-001</td>
<td>and [26]</td><td></td><td>= 4.250144186334534e-001</td><td>And in [64]</td><td>1</td><td>= 1.001463112557766e + 000</td>
<td>and [27]</td><td>1</td><td>= 4.42001394226934le-001</td><td>1 in [65]</td><td>1</td><td>= 1.006893331637123e + 000</td>
<td>and [28]</td><td>1</td><td>= 4.589582896478246e-001</td><td>1 in [66]</td><td>1</td><td>= 1.012508393574432e + 000</td>
<td>and [29]</td><td></td><td>= 4.758753745532750e-001</td><td>1 in [67]</td><td>1</td><td>= 1.017729040219375e + 000</td>
<td>and [30]</td><td>1</td><td>= 4.927463828072591e-001</td><td>1 in [68]</td><td>1</td><td>= 1.022470190536100e + 000</td>
<td>and [31)</td><td>1</td><td>= 5.095720854151864e-001</td><td>And in [69]</td><td></td><td>= 1.026615653698808e + 000</td>
<td>and [32]</td><td></td><td>= 5.263554446856779e-001</td><td>1 in [70]</td><td>1</td><td>= 1.030198648769593e + 000</td>
<td>and [33]</td><td>1</td><td>= 5.430990601899994e-001</td><td>1 in [71]</td><td>1</td><td>= 1.033205850580933e + 000</td>
<td>and [34]</td><td>1</td><td>= 5.598052330684253e-001</td><td>1 in [72]</td><td>1</td><td>= 1.035694432087486e + 000</td>
<td>and [35)</td><td></td><td>= 5.764734796907189e-001</td><td>1 in [73]</td><td>1</td><td>= 1.037683165297586e + 000</td>
<td>1 in [74]</td><td>1 = 1.039227995800217e + 000</td><td>1 in (112]</td><td>1</td><td>= 7.609051036128973e-001</td>
<td>1 in [75]</td><td>1 = 1.040349586463588e + 000</td><td>1 in [113]</td><td>1</td><td>= 7.455111681431031e-001</td>
<td>1 in [76]</td><td>1 = 1.041086497214721e + 000</td><td>| and [114]</td><td>1</td><td>= 7.298745530879272e-001</td>
<td>1 in [77]</td><td>1 = 1.041443375950143e + 000</td><td>1 in [115)</td><td>1</td><td>= 7.140087729493950e-001</td>
<td>1 in [78]</td><td>1 = 1.041434355650865e + 000</td><td>1 in [116]</td><td>1</td><td>= 6.979336851549095e-001</td>
<td>1 in [79]</td><td>I = 1.04104 3184 21617 le + OOO</td><td>1 in [117J</td><td>1</td><td>= 6.816667882498023e-001</td>
<td>1 in [80]</td><td>1 = 1.040262316588456e + 000</td><td>1 in [118]</td><td>1</td><td>= 6.652304141388827e-001</td>
<td>1 in [81]</td><td>1 = 1.039061496136853e + 000</td><td>1 in [119]</td><td>1</td><td>= 6.486437667370537e-001</td>
<td>1 in [82]</td><td>1 = 1.037422300157921e + 000</td><td>1 in [120]</td><td>1</td><td>= 6.319284031798550e-001</td>
<td>1 in [83] ·</td><td>1 = 1.035311720204252e + 000.</td><td>1 in [121]</td><td></td><td>= 6.151031151692835e-001</td>
<td>1 in [84]</td><td>1 = 1.032712952177121e + 000</td><td>1 in [122]</td><td>1</td><td>= 5.981877665956570e-001</td>
<td>1 in [85]</td><td>1 = 1.029600494883906e + 000</td><td>And in [123]</td><td>1</td><td>= 5.811992722116214e-001</td>
<td>1 in [86]</td><td>1 = 1.025966756910904e + 000</td><td>And in (124)</td><td>1</td><td>= 5.641522833259215e-001</td>
<td>1 in [87]</td><td>1 = 1.021798805583990e + 000</td><td>1 in [125]</td><td>1</td><td>= 5.470652177576862e-001</td>
<td>1 in [88]</td><td>1 = 1.017100128250049e + 000</td><td>And in [126]</td><td>1</td><td>= 5.299509559653194e-001</td>
<td>1 in [89]</td><td>1 = 1.011867706519706e + 000</td><td>1 in [127]</td><td>1</td><td>= 5.128557121424191e-001</td>
<td>1 in [90]</td><td>1 = 1.006109248754940e + 000</td><td>1 in [128]</td><td>1</td><td>= 4.956175421414453e-001</td>
<td>1 in [91)</td><td>1 = 9.998285752401580e-001</td><td>1 in [129]</td><td>.1</td><td>= 4.782650346610896e-001</td>
<td>1 in [92)</td><td>1 = 9.930379854679836e-001</td><td>1 in [130]</td><td>1</td><td>= 4.609828932783459e-001</td>
<td>1 in [93]</td><td>1 = 9.857387823493258e-001</td><td>1 in [131J</td><td></td><td>= 4.437530233023859e-001</td>
<td>1 in [94]</td><td>1 = 9.779405164766706e-001</td><td>1 in [132]</td><td>1</td><td>= 4.26595024646544Oe-001</td>
<td>1 in [95]</td><td>1 = 9.696426101291272e-001</td><td>And in [133]</td><td>1</td><td>= 4.095160467543179e-001</td>
<td>1 in [96]</td><td>I = 9.608519516143015e-001</td><td>1 in [134]</td><td>1</td><td>= 3.925409172155113e-001</td>
<td>1 in [97]</td><td>I = 9.515674613550604e-001</td><td>1 in [135]</td><td>1</td><td>= 3.756821671788237e-001</td>
<td>1 in [98]</td><td>I = 9.417975696327747e-001</td><td>1 in [136]</td><td>1</td><td>= 3.589626517817934e-001</td>
<td>1 in [99]</td><td>I = 9.315442093447622e-001</td><td>1 in [137]</td><td>1</td><td>= 3.423942311297658e-001</td>
<td>in 100]</td><td>I = 9.208194746232827e-001</td><td>1 in [138]</td><td>1</td><td>= 3.259993851088293e-001</td>
<td>and [101]</td><td>1 = 9.096310803629866e-001</td><td>1 in [139]</td><td>1</td><td>= 3.09786180597382le-001</td>
<td>and [102]</td><td>| = 8.979959173503500e-001</td><td>1 in [140]</td><td>1</td><td>= 2.937724988593393e-001</td>
<td>and [103]</td><td>1 = 8.859232320517536e-001</td><td>1 in [141]</td><td>1</td><td>= 2.779637821990255e-001</td>
<td>and [104]</td><td>1 = 8.734366852542127e-001</td><td>And in [142]</td><td>1</td><td>= 2.62374915948804le-001</td>
<td>and [105]</td><td>1 = 8.605542791988831e-001</td><td>1 in [143]</td><td>1</td><td>= 2.470098299603623e-001</td>
<td>and [106]</td><td>| = 8.472987145504696e-001</td><td>And in [144]</td><td>1</td><td>= 2.318815478758375e-001</td>
<td>and [107]</td><td>1 = 8.336863467961255e-001</td><td>And in [145]</td><td></td><td>= 2.169925682529340e-001</td>
<td>and [108]</td><td>1 = 8.197387292306723e-001</td><td>And in [146]</td><td>1</td><td>= 2.023548005388463e-001</td>
<td>and [109]</td><td>1 = 8.054701312929008e-001</td><td>And in [147]</td><td>1</td><td>= 1.879711746686855e-001</td>
<td>and [110]</td><td>1 = 7.908995350037713e-001</td><td>And in [148]</td><td></td><td>= 1.738542127021508e-001</td>
<td>and [III]</td><td>1 = 7.760385598209244e-001</td><td>| and [149]</td><td>1</td><td>= 1.600061812296078e-001</td>
<td>and [150]</td><td>1</td><td>= 1.464389150679625e-001</td><td>1 in [18B]</td><td>1</td><td>= 1.261262023246478e-001</td>
<td>and [151]</td><td>1</td><td>= 1.331544923127771e-001</td><td>1 in [189]</td><td>1</td><td>= 1.268280540744526e-001</td>
<td>and [152]</td><td>1</td><td>= 1.201628679722633e-001</td><td>1 in [190]</td><td>1</td><td>= 1.272498700590511e-001</td>
<td>and [153]</td><td>1</td><td>= 1.074630704470568e-001</td><td>1 in [191]</td><td>1</td><td>= 1.273590703506806e-001</td>
<td>and [154]</td><td>1</td><td>= 9.506966959632511e-002</td><td>1 in [192]</td><td>1</td><td>= 1.274567595465545e-001</td>
<td>and [155]</td><td>1</td><td>= 8.298103104739203e-002</td><td>1 in [193]</td><td>1</td><td>= 1.275561350483646e-001</td>
<td>and [156]</td><td>1</td><td>= 7.120356992726613e-002</td><td>1 in [194]</td><td>1</td><td>= 1.273648326872248e-001</td>
<td>and [157]</td><td>1</td><td>= 5.973741829536090e-002</td><td>1 in [195]</td><td>1</td><td>= 1.269415772180714e-001</td>
<td>and [158]</td><td>1</td><td>- 4.85900576701681le-002</td><td>1 in [196)</td><td>1</td><td>= 1.262995646340671e-001</td>
<td>and [159]</td><td>1</td><td>= 3.775928110298274e-002</td><td>1 in [197]</td><td></td><td>= 1.254605188749804e-001</td>
<td>and [160]</td><td>1</td><td>= 2.726484300186575e-002</td><td>1 in [198]</td><td>1</td><td>= 1.244269583009826e-001</td>
<td>and [161]</td><td>1</td><td>e 1.711323992709580e-002</td><td>1 in [199]</td><td>1</td><td>= 1.232131583108813e-001</td>
<td>and [162]</td><td>1</td><td>= 7.298197371320593e-003</td><td>And in [200]</td><td>1</td><td>= 1.218183974842866e-001</td>
<td>and [163]</td><td>1</td><td>=. 2.184256929356781e-003</td><td>1 in [201]</td><td>1</td><td>= 1.202545652840080e-001</td>
<td>and [164]</td><td>1</td><td>= 1.132324047372148e-002</td><td>1 in [202]</td><td>1</td><td>= 1.185243106889108e-001</td>
<td>and [165]</td><td>1</td><td>= 2.012236990754980e-002</td><td>And in [2O3]</td><td>1</td><td>= 1.1663991O2636992e-Ol</td>
<td>and [166]</td><td>1</td><td>= 2.857528272530154e-002</td><td>And in [204]</td><td>1</td><td>= 1.146042249339280e-001</td>
<td>and [167]</td><td>1</td><td>= 3.666942822678171e-002</td><td>1 in [205]</td><td>1</td><td>= 1.124296184976912e-001</td>
<td>and [168]</td><td>1</td><td>= 4.439683978044157e-002</td><td>And in [206]</td><td>1</td><td>= 1.101215600923314e-001</td>
<td>and [169]</td><td>1</td><td>= 5.177964768870787e-002</td><td>And in [207]</td><td></td><td>= 1.076972053405737e-001</td>
<td>and [170]</td><td>1</td><td>= 5.881296711410786e-002</td><td>1 in [208]</td><td>1</td><td>= 1.051641975499523e-001</td>
<td>and [171]</td><td>1</td><td>= 6.550209046893848e-002</td><td>1 in [2O9]</td><td>1</td><td>= 1.025397604985405e-001</td>
<td>and [172]</td><td>1</td><td>= 7.184073822817207e-002</td><td>1 in [210]</td><td>1</td><td>= 9.982957934346254e-002</td>
<td>and [173]</td><td>1</td><td>= 7.783299328224960e-002</td><td>1 in [211]</td><td>1</td><td>= 9.705239536075722e-002</td>
<td>and [174]</td><td>1</td><td>= 8.347150698567406e-002</td><td>1 in [212]</td><td>1</td><td>= 9.421624116597689e-002</td>
<td>and [175]</td><td>1</td><td>= 8.875756217893037e-002</td><td>1 in [213]</td><td>1</td><td>= 9.133590931873967e-002</td>
<td>and [176]</td><td>1</td><td>= 9.368651761350569e-002</td><td>1 in [214]</td><td>1</td><td>= 8.841813387276727e-002</td>
<td>and [177]</td><td>1</td><td>= 9.826251129465624e-002</td><td>1 in [215]</td><td>1</td><td>= 8.547715661443602e-002</td>
<td>and [178]</td><td>1</td><td>= 1.024804711677230e-001</td><td>And in [216]</td><td>1</td><td>= 8.251962055343706e-002</td>
<td>and [179]</td><td>1</td><td>= 1.063454554357498e-001</td><td>1 in [217]</td><td>1</td><td>= 7.955570759229536e-002</td>
<td>and [180]</td><td>1</td><td>= 1.098551252869576e-001</td><td>1 in [218]</td><td>1</td><td>= 7.657649751612349e-002</td>
<td>and [181]</td><td>1</td><td>= 1.130180022553412e-001</td><td>1 in [219]</td><td>1</td><td>= 7.360559211914287e-002</td>
<td>and [182]</td><td>1</td><td>= 1.158358935177899e-001</td><td>1 in [220]</td><td>1</td><td>= 7.064948295960993e-002</td>
<td>and [183)</td><td>1</td><td>= 1.183233335449968e-001</td><td>1 in [221]</td><td>Ί</td><td>= 6.771675107480543e-002</td>
<td>and [184]</td><td>1</td><td>= 1.204854506722672e-001</td><td>1 in [222]</td><td>1</td><td>= 6.480448458935215e-002</td>
<td>and [185]</td><td>1</td><td>= 1.223371395264402e-001</td><td>1 in [223]</td><td></td><td>= 6.192692754258131e-002</td>
<td>and [186]</td><td>1</td><td>= 1.238868653862843e-001</td><td>And in [224]</td><td>1</td><td>= 5.911363249658311e-002</td>
<td>and [187]</td><td>1</td><td>= 1.251477258491527e-001</td><td>1 in [225]</td><td>1</td><td>= 5.637219228757212e-002</td>
<td>and [226]</td><td>1</td><td>= 5.368313072045600e-002</td><td>1 in [264]</td><td>1</td><td>= 5.063851046064050e-003</td>
<td>and [227]</td><td>1</td><td>= 5.105620793438655e-002</td><td>1 in [265]</td><td>1</td><td>= 4.754191853611012e-003</td>
<td>and [228]</td><td>1</td><td>= 4.849284995895640e-002</td><td>1 in [266]</td><td>1</td><td>= 4.448993249380505e-003</td>
<td>and [229]</td><td>1</td><td>= 4.599068181839981e-002</td><td>1 in [267]</td><td>1</td><td>= 4.133639756278191e-003</td>
<td>and [230]</td><td>1</td><td>= 4.35556858889884le-002</td><td>1 in [268]</td><td>1</td><td>= 3.811612348723333e-003</td>
<td>and [231]</td><td>1</td><td>= 4.125570251909672e-002</td><td>1 in [269]</td><td>1</td><td>= 3.505531318950422e-003</td>
<td>and [232]</td><td>1</td><td>= 3.907137550527191e-002</td><td>1 in [270]</td><td>1</td><td>= 3.209092846617964e-003</td>
<td>wΓ2331</td><td>1</td><td>= 3.696342556744636p-n0?</td><td rowspan="2">1 uf2711 ... <sub>L</sub> . · * J</td><td>1</td><td>- 9 Q971 Π1</td>
<td></td><td></td><td></td><td>1</td><td></td>
<td>and [234]</td><td>1</td><td>= 3.493300140502248e-002</td><td>1 in [272]</td><td>1</td><td>= 2.653818578698405e-003</td>
<td>and [235]</td><td>1</td><td>= 3.298151059524886e-002</td><td>1 in [273]</td><td>1</td><td>= 2.396404013961463e-003</td>
<td>and [236]</td><td>1</td><td>= 3.110861245410919e-002</td><td>And in [274]</td><td>1</td><td>= 2.152379960589273e-003</td>
<td>and [237]</td><td>1</td><td>= 2.931525594774175e-002</td><td>| and [275]</td><td>1</td><td>= 1.924844672908215e-003</td>
<td>and [238]</td><td>1</td><td>= 2.760090729801069e-002</td><td>And in [276]</td><td>1</td><td>= 1.699160580023900e-003</td>
<td>and [239]</td><td>1</td><td>= 2.597956638848436e-002</td><td>1 in [277]</td><td>1</td><td>= 1.480542563288228e-003</td>
<td>and [240]</td><td>1</td><td>= 2.443433592149451e-002</td><td>And in [278J</td><td></td><td>= 1.283280633901446e-003</td>
<td>and [241)</td><td>1</td><td>= 2.296470793543091e-002</td><td>And in [279]</td><td>1</td><td>= 1.131859661378862e-003</td>
<td>and [242]</td><td></td><td>= 2.156304510969632e-002</td><td>1 in [280]</td><td>1</td><td>= 9.730460256556873e-004</td>
<td>and [243]</td><td>1</td><td>= 2.023524610221679e-002</td><td>And in [281]</td><td>1</td><td>= 7.677634115875747e-004</td>
<td>and [244]</td><td>1</td><td>= 1.897505817503749e-002</td><td>1 in [282]</td><td>1</td><td>= 5.599347984905645e-004</td>
<td>in [.245]</td><td>1</td><td>= 1.778248750467421e-002</td><td>And in [283]</td><td>1</td><td>= 3.337966579125254e-004</td>
<td>and [246]</td><td>1</td><td>= 1.665187994388476e-002</td><td>1 in [284]</td><td>1</td><td>= 9.099722643476421e-005</td>
<td>and [247]</td><td>1</td><td>= 1.557759513377242e-002</td><td>1 in [285]</td><td>1</td><td>= 1.498231621816O41e-OO4</td>
<td>and [248]</td><td>1</td><td>= 1.456208586604537e-002</td><td>1 in [286]</td><td>1</td><td>= 4.366447012116811e-004</td>
<td>and [249]</td><td>1</td><td>= 1.361072086117313e-002</td><td>1 in [287]</td><td>1</td><td>= 6.307841647560053e-004</td>
<td>and [250]</td><td>1</td><td>= 1.270747042064656e-002</td><td>1 in [288]</td><td>1</td><td>= 6.150316826138937e-004</td>
<td>and [251]</td><td>1</td><td>= 1.186210743261470e-002</td><td>And in [289]</td><td>1</td><td>= 8.990255827053560e-004</td>
<td>and [252]</td><td>1</td><td>= 1.106958962776399e-002</td><td>And in [290]</td><td>1</td><td>= 1. 232134364570107e-003</td>
<td>and [253]</td><td>1</td><td>= 1.033126278863177e-002</td><td>1 in [291]</td><td>1</td><td>= 1.471167206249042e-003</td>
<td>and [254]</td><td>1</td><td>= 9.640298325700842e-003</td><td>1 in [292]</td><td>1</td><td>= 1.697652664777771e-003</td>
<td>and [255]</td><td>1</td><td>= 8.996371481700806e-003</td><td>1 in [293]</td><td>1</td><td>= 1.985825255428654e-003</td>
<td>and [256]</td><td>1</td><td>= 8.407748878436545e-003</td><td>And in [294]</td><td>1</td><td>= 2.172866052963961e-003</td>
<td>and [257]</td><td>1</td><td>= 7.876393114319395e-003</td><td>And in [295]</td><td></td><td>= 1.812176023993582e-003</td>
<td>and [258]</td><td>1</td><td>= 7.380543918629573e-003</td><td>1 in [296]</td><td>1</td><td>= 1.344657262814793e-003</td>
<td>and [259]</td><td>1</td><td>= 6.925141135202262e-003</td><td>1 in [297]</td><td>1</td><td>= 9.373975348172919e-004</td>
<td>and [26o)</td><td></td><td>= 6.500502521462604e-003</td><td>And in [298]</td><td>1</td><td>= 5.621720998949145e-004</td>
<td>and [261]</td><td>1</td><td>= 6.109178606718115e-003</td><td>1 in [299]</td><td>1</td><td>= 2.048498552413189e-004</td>
<td>in the {262]</td><td>1</td><td>= 5.741103163221257e-003</td><td>And in [300]</td><td>1</td><td>= 2.004822830002534e-004</td>
<td>and [263]</td><td>1</td><td>= 5.394569608919965e-003</td><td>And in [301]</td><td></td><td>= 6.169854804735951e-004</td>
And in [302] | = 1.061498982103114e-003 | in [303] | = 1.594860949611097e-003 And in [304] | = 2! 24647831574725e-003 I in [305] | = 2.621537051750861e-003 And in [306] I = 3.064311083207632e-003 I in [307] | = 3.460362845825662e-003 And in [308] | = 3.794425324215804e-003 And in [309] = 4.091032597247918e-003 And in [310] | = 4.369553676668050e-003 I in [311] | = 4.554811297024067e-003 And in [312] I = 4.663276675479689e-003 And in [313] | = 4.722567636185647e-003 | in [314] | = 4.704321497976561e-003 And in [315] | = 4.636227793039124e-003 I in [316] I = 4.517190210387324e-003 And in [317] | = 4.351667566540186e-003 And in [318] | = 4.135130493071822e-003 And in [319] I = 3.870851645947402e-003 And in [320] | = 3.597475533950260e-003 And in [321] | = 3.318857985461042e-003 And in [322] | = 3.000422543655664e-003 And in [323] | = 2.658042081080524e-003 And in [324] | = 2.292813563887493e-003 I in [325] I = 1. 914114740669928e-003 I in [326] | = 1.525818616748839e-003 And in [327] | = 1! 56680209049319e-003 And in [328] | = 7.804546272743493e-004 And in [329] I = 4.268574601396473e-004 I in [330] | = 1.324291707264515e-004 And in [331] | = 1.218226450050751e-004 And in [332] | = 3.189336138130849e-004 And in [333] | = 4.749931197951235e-004 | in [334] | = 5.970696819774243e-004 | in [335] | = 6.673250213055329e-004 And in [336] I = 6.887783835812338e-004 And in [337] | = 6.766320515830324e-004 | in [338] | = 6.944123176012471e-004 And in [339] I = 7.139919634325070e-004 970696819774243e-004 | in [335] | = 6.673250213055329e-004 And in [336] I = 6.887783835812338e-004 And in [337] | = 6.766320515830324e-004 | in [338] | = 6.944123176012471e-004 And in [339] I = 7.139919634325070e-004 970696819774243e-004 | in [335] | = 6.673250213055329e-004 And in [336] I = 6.887783835812338e-004 And in [337] | = 6.766320515830324e-004 | in [338] | = 6.944123176012471e-004 And in [339] I = 7.139919634325070e-004
And in [340] I = 7.154123487609100e-004 I in [341] | = 7.376101027486600e-004 And in [342] | = 6.976561203768226e-004 And in [343] | = 5.721223454434728e-004 And in [344] | = 2.934875643581191e-004 And in [345] | = 1.092526149391273e-004 And in [346] j = 6.415402443848103e-004 And in [347] | = 1.194730618383423e-003 And in [348] | = 1.557112059887280e-003 And in [349] | = 1.891971801393744e-003 And in [350] | = 2.225524159129023e-003 And in [351] | = 2.530906981099261e-003 And in [352] I = 2.719749515067397e-003 And in [353] | = 2.729136737522100e-003 I in [354] | = 2.703019498899013e-003 And in [355] I = 2.630471852319136e-003 I in [356] | = 2.470456304276468e-003 and in [357] | = 2.239142906871446e-003 And in [358] I = 2.033465291493264e-003 I in [359] | = 1.948069005335563e-003 And in [360] | = 1.725029670030533ee-003 And in [361] | = 1.417366709895927e-003 And in [362] | = 1! 27141815310061e-003 And in [363] I = 8. 196637962311630e-003 | in [373] | = 1.292865844760059e-003 | in [374] I = 1.146268465739874e-003 | in [375] I = 1.040598055074471e-003 | in [376] | = 9.767709065548874e-004 | in [377] I = 9.294665200453614e-004 196637962311630e-003 | in [373] | = 1.292865844760059e-003 | in [374] I = 1.146268465739874e-003 | in [375] I = 1.040598055074471e-003 | in [376] | = 9.767709065548874e-004 | in [377] I = 9.294665200453614e-004
<td>in [378] |</td><td>= 9.862027119530482e-004</td><td>1 in [416] |</td><td>= 5.901617707607606e-007</td>
<td>in [379] ί</td><td>= 1.047654674829846e-003</td><td>1 in [417] |</td><td>= 1.831121301698088e-004</td>
<td>in [380]</td><td>= 1.099000599887377e-003</td><td>1 in [418] |</td><td>= 9.755685190624611e-005</td>
<td>in [381] 1</td><td>= 1.151795860160292e-003</td><td>1 in [419] |</td><td>= 6.606461762989423e-005</td>
<td>in [382] |</td><td>= 1.194743370333155e-003</td><td>1 in [420]</td><td>= 3.799971890923797e-005</td>
<td>in [383] |</td><td>= 1.250742797799558e-003</td><td>1 in [421] |</td><td>= 4.150075391929448e-005</td>
<td>in [384] |</td><td>= 1.287819050086379e-003</td><td>1 in [422] |</td><td>= 5.021905476506264e-005</td>
<td>..f 'inc ii</td><td></td><td></td><td></td>
<td>At tOOJJ |</td><td>- X.ZDJlOOOe-UUJ</td><td>1 WL ^ ZJJ and</td><td>= 5.8610001374J4 / lJe-UUb</td>
<td>in [386] |</td><td>= 1.226113111394085e-003.</td><td>1 in [424] |</td><td>= 2.126364641291926e-005</td>
<td>in [387] |</td><td>= 1.177515087338257e-003</td><td>1 in [425] |</td><td>= 1. 1810775827 97280e-00.4</td>
<td>in [388] 1</td><td>= 1.122503050159859e-003</td><td>1 in [426] |</td><td>= 9.990757789944374e-005</td>
<td>in [389]</td><td>= 1.089428846944533e-003</td><td>1 in [427] |</td><td>= 1.035782617124906e-004</td>
<td>in [390] |</td><td>= 1.054963366189962e-003</td><td>1 in [428] |</td><td>= 8.870181845310037e-005</td>
<td>in [391] |</td><td>= 9.019128558297515e-004</td><td>1 in [429] |</td><td>= 5.533953373249822e-005</td>
<td>in [392] |</td><td>= 7.847839620863715e-004</td><td>1 in [430] |</td><td>= 1.580188994455254e-005</td>
<td>in [393] |</td><td>= 6.205675927856794e-004</td><td>1 in [431] 1</td><td>= 1.277184430250593e-006</td>
<td>in [394] |</td><td>= 3.157663628445906e-004</td><td>1 in [432] |</td><td>= 5.009913312943629e-006</td>
<td>in [395] 1</td><td>= 2.556449844935384e-004</td><td>1 in [433] |</td><td>= 1.499170392246774e-005</td>
<td>in [396] |</td><td>= 2.520606580606257e-004</td><td>1 in [434] |</td><td>= 2.241545750231630e-005</td>
<td>in [397] |</td><td>= 2.346980949474655e-004</td><td>1 in [435] |</td><td>= 3.628511258723260e-005</td>
<td>in [398] |</td><td>= 2.060394037017961e-004</td><td>1 in [436] |</td><td>= 2.406516798531014e-005</td>
<td>in [399] |</td><td>= 1.635905995590986e-004</td><td>1 in [437] |</td><td>= 2.515118233957011e-005</td>
<td>in [400] |</td><td>= 1.176237128375623e-004</td><td>1 in [438] |</td><td>= 3.759629789955498e-005</td>
<td>in [401] |</td><td>= 6.193369904730005e-005</td><td>Ί in [439] |</td><td>= 5.40815454312412le-005</td>
<td>in [402] |</td><td>= 3.568554800150508e-005</td><td>1 in [44O] |</td><td>= 4.493916063285122e-005</td>
<td>in [403] |</td><td>= 2.443161189273522e-005</td><td>1 in [441] |</td><td>= 2.806963579578946e-005</td>
<td>in [404] |</td><td>= 1.334090914042349e-005</td><td>1 in [442], |</td><td>= 2.364518513682831e-005</td>
<td>in [405] |</td><td>= 2.853437194757816e-006</td><td>1 in [443J 1</td><td>= 1.260639764582286e-005</td>
<td>in [406] |</td><td>= 1.039263591111469e-004</td><td>1 in [444] |</td><td>= 2.5994677726O3631e-008</td>
<td>in [407] |</td><td>= 5.144969377044875e-005</td><td>as above [445]</td><td>= 1.774108392496017e-005</td>
<td>in [408] 1</td><td>= 9.711681816385056e-005</td><td>1 in [446] |</td><td>= 5.889276659458115e-006</td>
<td>in [409] 1</td><td>= 2.472023910553232e-005</td><td>1 in [447] |</td><td>= 4.663777919108619e-005</td>
<td>in [410] |</td><td>= 5.397064424090302e-005</td><td>1 in [448] |</td><td>= 2.078886359425321e-004</td>
<td>in [411] 1</td><td>= 6.487880719449901e-005</td><td>1 in [449] |</td><td>= 2.131405580107761e-004</td>
<td>in [412] |</td><td>= 5.192444140699947e-005</td><td>1 in [450] |</td><td>= 1.784192600231068e-004</td>
<td>in [413] 1</td><td>= 9.204876089551197e-005</td><td>1 in [451] |</td><td>= 1.744841754193053e-004</td>
<td>in [414] |</td><td>= 1.815837353167847e-004</td><td>1 in [452] |</td><td>= 1.728672507238372e-004</td>
<td>in [415] 1</td><td>= 3.595054179561440e-004</td><td>1 in [453] |</td><td>= 1.885286127508226e-004</td>
<td>1 in [454]</td><td>1</td><td>= 2.078299015661617e-004</td><td>And in [492]</td><td></td><td>=</td><td>4.005269212731273e-005</td>
<td>1 in [455]</td><td>1</td><td>= 2.123671573189573e-004</td><td>| and [493]</td><td>1</td><td>=</td><td>2.461876679726978e-005</td>
<td>| and [456]</td><td>1</td><td>= 2.415166002501312e-004</td><td>And in [494]</td><td>1</td><td>=</td><td>4.469729032194765e-006</td>
<td>And in [457]</td><td>1</td><td>= 2.217025456251449e-004</td><td>| and [495]</td><td>1</td><td>=</td><td>3.798519731621893e-007</td>
<td>| and [458]</td><td>1</td><td>= 9.907630821710970e-005</td><td>And in [496]</td><td>1</td><td>=</td><td>1.374896222030490e-006</td>
<td>1 in [459]</td><td>1</td><td>= 8.039231481768845e-005</td><td>| and [497]</td><td>1</td><td>=</td><td>3.965363805500215e-006</td>
<td>| and [460]</td><td>1</td><td>= 7.934509417722400e-005</td><td>And in [498]</td><td>1</td><td>=</td><td>7.300588863934780e-006</td>
<td>i. 4 61j</td><td>and</td><td>= 5.6M199358 / 80iuó-uu5</td><td>1 W1499]</td><td>1</td><td>=</td><td>1.168894474770061e-005</td>
<td>1 in [462]</td><td>1</td><td>= 5.449816072329412e-005</td><td>And in [500]</td><td>1</td><td>=</td><td>8.563819899447630e-006</td>
<td>1 in (463]</td><td>1</td><td>= 4.489491034408147e-005</td><td>And in [501]</td><td>1</td><td>=</td><td>8.975977837330335e-006</td>
<td>And in [464]</td><td>1</td><td>= 3.49828598235998le-005</td><td>And in [502]</td><td>1</td><td>=</td><td>2.800455533708622e-005</td>
<td>And in [465]</td><td>1</td><td>= 1.748284921486958e-005</td><td>And in [503]</td><td>1</td><td></td><td>2.015445311139832e-005</td>
<td>And in [466]</td><td>1</td><td>= 9.075430772832575e-006</td><td>And in [504]</td><td></td><td>=</td><td>1.125134651175812e-005</td>
<td>| and [467]</td><td></td><td>= 1.052707430241351e-005</td><td>1 in [5O5]</td><td>1</td><td>=</td><td>5.869707265615299e-006</td>
<td>1 in [468]</td><td>1</td><td>= 6.538878366985722e-006</td><td>1 in [506]</td><td>1</td><td>=</td><td>1.013259758329981e-005</td>
<td>And in [469]</td><td>1</td><td>= 2.206341308073472e-005</td><td>1 in [507]</td><td>1</td><td>=</td><td>1.088325131492173e-005</td>
<td>1 in [470]</td><td>1</td><td>= 1.769261935287328e-004</td><td>| and [508]</td><td>1</td><td>=</td><td>7.167101260771279ę-006</td>
<td>| and [471]</td><td>1</td><td>= 6.418658561385058e-005</td><td>And in [509]</td><td>1</td><td>=</td><td>4.840577540089826e-006</td>
<td>And in [472]</td><td>1</td><td>= 8.882305312548962e-005</td><td>1 in [510]</td><td>1</td><td>=</td><td>1.469933448634890e-005</td>
<td>1 in [473]</td><td>1</td><td>= 1.721347222211949e-005</td><td>1 in [511]</td><td>1</td><td>=</td><td>8.010079089953001e-006</td>
<td>And in [474]</td><td>1</td><td>= 6.093372716385583e-005</td><td>And in [512]</td><td>1</td><td>=</td><td>3.299004046633323e-005</td>
<td>And in [475]</td><td>1</td><td>= 7.679955330373515e-005</td><td>And in [513]</td><td>1</td><td>=</td><td>4.373302115187172e-005</td>
<td>And in [476]</td><td>1</td><td>= 7.194151087015007e-005</td><td>1 in [514]</td><td>1</td><td>=</td><td>3.177468256997963e-005</td>
<td>| and [477]</td><td>1</td><td>= 7.245095937243279e-005</td><td>And in [515]</td><td>1</td><td>=</td><td>2.976824036182567e-005</td>
<td>And in (478]</td><td>1</td><td>= 7.870354371072524e-005</td><td>1 in [516]</td><td></td><td>=</td><td>2.464228015326852e-005</td>
<td>And in [479J</td><td>1</td><td>= 5.822201682995846e-004</td><td>1 in [517]</td><td>1</td><td>=</td><td>1.606050838620834e-005</td>
<td>And in (480)</td><td>1</td><td>= 2.666444630171025e-004</td><td>| and [518]</td><td>1</td><td>=</td><td>6.261944255489322e-006</td>
<td>| and [481]</td><td>1</td><td>= 7.872592352725688e-005</td><td>And in [519]</td><td>1</td><td>=</td><td>4.591009581217994e-007</td>
<td>1 in [482]</td><td>1</td><td>= 7.095836893185526e-005</td><td>1 in [520]</td><td>1</td><td>=</td><td>1.395220723090848e-005</td>
<td>And in [483]</td><td>1</td><td>= 5.643103068471008e-005</td><td>1 in [521]</td><td>1</td><td>=</td><td>1.622786214398703e-005</td>
<td>| and [484]</td><td>1</td><td>= 6.904415362098980e-005</td><td>| and [522]</td><td>1</td><td>=</td><td>2.043464113212971e-006</td>
<td>1 in (485)</td><td>1</td><td>= 4.694251739991356e-005</td><td>1 in [523]</td><td>1</td><td>=</td><td>1.653463907257247e-006</td>
<td>And in [486]</td><td></td><td>= 3.367998338617662e-005</td><td>1 in [524]</td><td>1</td><td>=</td><td>1.551250801467300e-008</td>
<td>And in [487J</td><td>Ί</td><td>= 6.481921021601837e-005</td><td>And in [525]</td><td>1</td><td>=</td><td>1.907927361317977e-006</td>
<td>| and [488]</td><td>1</td><td>= 6.582328030188790e-005</td><td>And in [526]</td><td>1</td><td>=</td><td>9.607068622268791e-007</td>
<td>And in [489]</td><td>1</td><td>= 4.256442530773449e-005</td><td>And in [527]</td><td>1</td><td>=</td><td>4.636105364510011e-007</td>
<td>| and [490]</td><td>1</td><td>= 4.939392400898679e-005</td><td>And in [528]</td><td>1</td><td>=</td><td>2.765649762593200e-007</td>
<td>And in [491]</td><td>1</td><td>= 5.272982009116034e-005</td><td>1 in [529]</td><td>1</td><td>=</td><td>1.922074581855119e-006</td>
<td>and [530]</td><td>1</td><td>= 9.897194091136331e-007</td><td>1 in [568]</td><td>1</td><td>= 2.714879009950152e-007</td>
<td>and [531]</td><td>1</td><td>= 7.873304717454037e-008</td><td>1 in [569]</td><td>1</td><td>= 2.567964804401197e-008</td>
<td>and [532]</td><td>1</td><td>= 2.945239208477290e-008</td><td>1 in [570]</td><td>1</td><td>= 2.041128570435378e-006</td>
<td>and [533]</td><td>1</td><td>= 2 - 757610624807679e-006</td><td>1 in [571]</td><td>1</td><td>= 3.262753594084781e-006</td>
<td>and [534]</td><td>1</td><td>= 1.402925247695813e-005</td><td>1 in [572]</td><td>1</td><td>= 3.567581483749161e-006</td>
<td>and [535]</td><td>1</td><td>= 9.388962780643742e-006</td><td>And in [573]</td><td>1</td><td>= 4.083718802566134e-006</td>
<td>and [536]</td><td>1</td><td>= 2.068297421740023e-005</td><td>And in [574]</td><td>1</td><td>= 5.364807253588177e-006</td>
<td rowspan="2">. . Γ Γ 1 wioo / j</td><td></td><td>. ______________- - - -</td><td></td><td></td><td></td>
<td>1</td><td>- i. ^ so ^ ooauzoaoziue-uu /</td><td>1 wio / bj</td><td>and</td><td>= 4.Ϊ78ϋ5ΰ ± 49Ó40Ż2Je-006</td>
<td>and [538]</td><td>1</td><td>= 6.757014945674924e-009</td><td>1 in [576]</td><td>1</td><td>= 5.189086332701670e-006</td>
<td>and [539]</td><td>1</td><td>= 2.778618354859861e-007</td><td>1 in [577]</td><td></td><td>= 3.357218747491756e-006</td>
<td>and [540]</td><td>and</td><td>= 1.569003268449803e-006</td><td>And in [578]</td><td>1</td><td>= 6.310207878018869e-006</td>
<td>and [541]</td><td>1</td><td>= 1.089500601234349e-006</td><td>| and [579]</td><td></td><td>= 5.924001540927652e-006</td>
<td>and [542]</td><td>1</td><td>= 9.870547653835426e-007</td><td>1 in [580]</td><td>1</td><td>= 5.161606640348293e-006</td>
<td>and [543]</td><td>1</td><td>= 3.867483283567218e-005</td><td>1 in [581]</td><td>1</td><td>= 3.377814811745950e-006</td>
<td>and [544]</td><td>1</td><td>= 1.232693496472088e-005</td><td>And in [582]</td><td>1</td><td>= 1.323267689777069e-006</td>
<td>and [545]</td><td>1</td><td>= 9.464782951082177e-007</td><td>] in [583]</td><td>1</td><td>= 1.074716688428712e-007</td>
<td>and [546]</td><td>1</td><td>= 8.254429452094225e-007</td><td>1 in [584]</td><td>1</td><td>= 3.561585382456484e-006</td>
<td>and [547]</td><td>1</td><td>= 4.883304950437536e-007</td><td>And in [585]</td><td>1</td><td>= 4.518603099564185e-006</td>
<td>and [548]</td><td>1</td><td>= 2.066961713890010e-007</td><td>1 in [586]</td><td>1</td><td>= 7.301956971603966e-007</td>
<td>and [549]</td><td>1</td><td>= 5.158212471036245e-009</td><td>1 in [587]</td><td>1</td><td>= 5.891904775161025e-007</td>
<td>and [550]</td><td>1</td><td>= 2.267731106642486e-007</td><td>1 in [588]</td><td>1</td><td>= 2.801882088134371e-008</td>
<td>and [551]</td><td>1</td><td>= 4.880844550713951e-008</td><td>And in [589]</td><td>1</td><td>= 6.322770332405526e-007</td>
<td>and [552]</td><td>1</td><td>= 3.361682183852576e-006</td><td>| and [590]</td><td>1</td><td>= 2.542598385847351e-007</td>
<td>and [553]</td><td>1</td><td>= 4.677015459111491e-006</td><td>1 in [591]</td><td>1</td><td>= .1.272704908592385e-007</td>
<td>and [554]</td><td>1</td><td>= 2.820292122791583e-008</td><td>1 in [592]</td><td>1</td><td>= 8.226599990523664e-008</td>
<td>and [555]</td><td>1</td><td>= 5.143614846654519e-007</td><td>And in [593]</td><td>1</td><td>= 5.433718768789140e-007</td>
<td>and [556]</td><td>1</td><td>= 3.818588614859347e-009</td><td>And in [594]</td><td>1</td><td>= 4.211177232106135e-007</td>
<td>and [557]</td><td>1</td><td>= 1.737276553950212e-007</td><td>1 in [595]</td><td>1</td><td>= 3.552991527555180e-008</td>
<td>and [558]</td><td>1</td><td>= 1.B76022048145804e-007</td><td>And in [596]</td><td>1</td><td>= 1.398913109540774e-008</td>
<td>and [559]</td><td>1</td><td>= 2.986488593070417e-009</td><td>1 in [597]</td><td>1</td><td>= 1.356727552196146e-006</td>
<td>and [560]</td><td>1</td><td>= 1.409927495646886e-008</td><td>1 in [598]</td><td>1</td><td>= 1.70694102Ó342299e-005</td>
<td>and [561]</td><td>1</td><td>= 6.977078748707401e-008</td><td>| and [599]</td><td>1</td><td>= 1.013575160981381e-005</td>
<td>and [562]</td><td>1</td><td>= 1.280675520205100e-008</td><td>And in [600]</td><td>1</td><td>= 2.285562946018590e-005</td>
<td>and [563]</td><td>1</td><td>= 2.222072007942510e-009</td><td>And in [601]</td><td>1</td><td>= 8.908041185396514e-008</td>
<td>and [564]</td><td>1</td><td>= 1.775191290895584e-009</td><td>And in [602]</td><td></td><td>= 9.597515277415496e-009</td>
<td>and [565]</td><td>1</td><td>= 1.686136654621906e-009</td><td>| and [603]</td><td>1</td><td>= 3.225913527455964e-007</td>
<td>and [566]</td><td>1</td><td>= 5.818594642226675e-006</td><td>| and [604]</td><td>1</td><td>= 1.070242712585309e-006</td>
<td>and [567]</td><td>1</td><td>= 2.150883991167946e-006</td><td>| and [605]</td><td>1</td><td>= 6.293002327021578e-007</td>
And in [606] | = 3.575650976036433ee-007 And in [607] | = 2.722295965060517e-005 I in [608] | = 8.676848186676888e-006 and in [609] | = 3.428660858940255e-007 And in [610] | = 4.767793949944890e-007 And in [611] | = 3.330981930777764e-007 And in [6.12] = 2.399696144635756e-007 And in [613] I = 7.326611439066549e-009 I in [614] | = 1.349943693297681e-007 And in [615] I = 5.393555749348494e-008 IW [616] | = 3.629067065524143e-006 And in [617] | = 5.690530948134642e-006 And in [618] | = 1.387566465624550e-008 And in [619] = 2.443085172403935e-007 I in [620] | = 1.723217058490933e-009 And in [621J | = 7.391973323448250e-008 and in [622] = 5.303527922331415e-008 And in [623] | = 8.883499047404846e-0Ϊ0 And in [624] | = 3.870536804891648e-009 I in [625] | = 1.846547564287500e-008 and in [626] | = 4.244090917065736e-009 And in [627] | = 4.013524925634108e-009 And in [628] = 6.325664562585882e-010 I in [629] | = 6. 025110605409611e-010 I in [630] | = 1.620171502086309e-006 And in [631] | = 5.490569954646963e-007 And in [632] | = 6.355303179925355e-008 and in [633] | = 5.426597100684762e-009 I in [634] I = 4.292861814894369e-007 I in [635] | = 6.834209542421138e-007 and in [636] = 7.099633014995863e-007 And in [637] | = 8.109951846981774e-007 I w (638) | = 4.118359768898598e-007 And in [639] | = 6.571760029213382e-007
<td>Annex 3</td><td></td><td></td><td></td><td></td><td>0.592</td><td><</td><td>and [36]</td><td><</td><td>0.594</td>
<td></td><td></td><td></td><td></td><td></td><td>0.609</td><td><</td><td>and [37]</td><td><</td><td>0611</td>
<td>0.010</td><td><</td><td>a [0]</td><td><</td><td>0012</td><td>0.625</td><td><</td><td>and [38]</td><td><</td><td>0.627</td>
<td>0.023</td><td><</td><td>in [l]</td><td><</td><td>0.025</td><td>0.642</td><td><</td><td>and [39]</td><td><</td><td>0.644</td>
<td>0.034</td><td><</td><td>in [2]</td><td><</td><td>0.036</td><td>0.658</td><td><</td><td>in [40]</td><td><</td><td>0.660</td>
<td>0.045</td><td><</td><td>in [3]</td><td><</td><td>0.047</td><td>0674</td><td><</td><td>in [41]</td><td><</td><td>0.676</td>
<td>0.058</td><td><</td><td>in [4]</td><td><</td><td>0.060</td><td>. 0.690</td><td><</td><td>and [42]</td><td><</td><td>0692</td>
<td>0.072</td><td><</td><td>and [5]</td><td><</td><td>0.074</td><td>0.706</td><td><</td><td>and [43]</td><td><</td><td>0.708</td>
<td>0.087</td><td><</td><td>in [6]</td><td><</td><td>0089</td><td>0722</td><td><</td><td>in [44]</td><td><</td><td>0.724</td>
<td>0.103</td><td><</td><td>in [7]</td><td><</td><td>0.105</td><td>0738</td><td><</td><td>and [45]</td><td><</td><td>0740</td>
<td>0.120</td><td><</td><td>in [8]</td><td><</td><td>0.122</td><td>0753</td><td><</td><td>and [46]</td><td><</td><td>0755</td>
<td>0.137</td><td><</td><td>in [9]</td><td><</td><td>0.139</td><td>0.769</td><td><</td><td>and [47]</td><td><</td><td>0.771</td>
<td>0.154</td><td><</td><td>and [10]</td><td><</td><td>0.156</td><td>0.784</td><td><</td><td>in [4 8]</td><td><</td><td>0786</td>
<td>0.171</td><td><</td><td>in [ll]</td><td><</td><td>0.173</td><td>0.799</td><td><</td><td>in [49]</td><td><</td><td>0801</td>
<td>0.188</td><td><</td><td>and [12]</td><td><</td><td>0.190</td><td>0.815</td><td><</td><td>and [50]</td><td><</td><td>0817</td>
<td>0.205</td><td><</td><td>and [13]</td><td><</td><td>0.207</td><td>0.830</td><td><</td><td>and [51]</td><td><</td><td>0832</td>
<td>0.222</td><td><</td><td>in [14]</td><td><</td><td>0.224</td><td>0.B45</td><td><</td><td>and [52]</td><td><</td><td>0847</td>
<td>0.239</td><td><</td><td>and [15]</td><td><</td><td>0.241</td><td>0.860</td><td><</td><td>and [53]</td><td><</td><td>0862</td>
<td>0.256</td><td><</td><td>and [16]</td><td><</td><td>0.258</td><td>0.874</td><td><</td><td>and [54]</td><td><</td><td>0876</td>
<td>0.272</td><td><</td><td>and [17]</td><td><</td><td>0.274</td><td>0.889</td><td><</td><td>and [55]</td><td><</td><td>0891</td>
<td>0.289</td><td><</td><td>and [18]</td><td><</td><td>0.291</td><td>0.903</td><td><</td><td>and [56]</td><td><</td><td>0.905</td>
<td>0.306</td><td><</td><td>and [19]</td><td><</td><td>0.308</td><td>0917</td><td><</td><td>and [57]</td><td><</td><td>0.919</td>
<td>0323</td><td><</td><td>and [20]</td><td><</td><td>0.325</td><td>0.930</td><td><</td><td>and [58]</td><td><</td><td>0.932</td>
<td>0.339</td><td><</td><td>and [21]</td><td><</td><td>0.341</td><td>0.943</td><td><</td><td>and [59]</td><td><</td><td>0945</td>
<td>0.356</td><td><</td><td>and [22]</td><td><</td><td>0358</td><td>0956</td><td><</td><td>and [60]</td><td><</td><td>0958</td>
<td>0.373</td><td><</td><td>and [23]</td><td><</td><td>0.375</td><td>- 0.968</td><td><</td><td>and [61]</td><td><</td><td>0.970</td>
<td>0.390</td><td><</td><td>and [24]</td><td><</td><td>0.392</td><td>0980</td><td><</td><td>and [62]</td><td><</td><td>0.982</td>
<td>0.407</td><td><</td><td>and [25]</td><td><</td><td>0.409</td><td>0.992</td><td><</td><td>and [63]</td><td><</td><td>0994</td>
<td>0.424</td><td><</td><td>and [26]</td><td><</td><td>0.426</td><td>1,000</td><td><</td><td>and [64]</td><td><</td><td>1.002</td>
<td>0441</td><td><</td><td>and [27]</td><td><</td><td>0443</td><td>1006</td><td><</td><td>in [65]</td><td><</td><td>1008</td>
<td>0.458</td><td><</td><td>and [28]</td><td><</td><td>0.460</td><td>1,012</td><td><</td><td>and [66]</td><td><</td><td>1.014</td>
<td>0.475</td><td><</td><td>in (29]</td><td><</td><td>0477</td><td>1,017</td><td><</td><td>and [67]</td><td><</td><td>1,019</td>
<td>. 0.492</td><td><</td><td>and [30]</td><td><</td><td>0.494</td><td>1,021</td><td><</td><td>and [68]</td><td><</td><td>1.023</td>
<td>0.509</td><td><</td><td>and [31]</td><td><</td><td>0.511</td><td>1,026</td><td><</td><td>and [69]</td><td><</td><td>1.028</td>
<td>0525</td><td><</td><td>in [32]</td><td><</td><td>0527</td><td>1.029</td><td><</td><td>and [70]</td><td><</td><td>1.031</td>
<td>0542</td><td><</td><td>and [33]</td><td><</td><td>0544</td><td>. 1,032</td><td><</td><td>and [71]</td><td><</td><td>1034</td>
<td>0.559</td><td><</td><td>and [34]</td><td><</td><td>0.561</td><td>1.035</td><td><</td><td>and [72]</td><td><</td><td>1.037</td>
<td>0.575</td><td><</td><td>and [35]</td><td><</td><td>0.577</td><td>1.037</td><td><</td><td>and [73]</td><td><</td><td>1.039</td>
ο ο
ο ο
ο ο
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0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
<td>, 038</td><td><in [74]</td><td><</td><td>1,040</td><td>0.760</td><td><</td><td>and [112]</td><td><</td><td>0.762</td>
<td>, 039</td><td><w [75]</td><td><</td><td>1.041</td><td>0745</td><td><</td><td>and [113]</td><td><</td><td>0.747</td>
<td>, 040</td><td><w [76]</td><td><</td><td>1,042</td><td>0729</td><td><</td><td>and [114]</td><td><</td><td>0731</td>
<td>, 040</td><td><in [77]</td><td><</td><td>1,042</td><td>0.713</td><td><</td><td>and [115]</td><td><</td><td>0.715</td>
<td>, 040</td><td><w [78]</td><td><</td><td>1,042</td><td>0.697</td><td><</td><td>and [116]</td><td><</td><td>0699</td>
<td>, 040</td><td><w [79]</td><td><</td><td>1,042</td><td>0.681</td><td><</td><td>and [117]</td><td><</td><td>0683</td>
<td>, 039</td><td><in [80]</td><td><</td><td>1.041</td><td>0664</td><td><</td><td>and [118]</td><td><</td><td>0666</td>
<td>, 038</td><td>s ... rc 11</td><td></td><td>1 η? Ι λ</td><td>n</td><td></td><td>,, FNM</td><td>✓</td><td>n this</td>
<td></td><td>'yr <sub>L</sub> w * j</td><td></td><td>X · V 1 V</td><td>V. V »u</td><td>• X</td><td>W [l ^ J</td><td></td><td>V · UJ V</td>
<td>, 036</td><td><w [82]</td><td><</td><td>1038</td><td>0631</td><td><</td><td>and [120]</td><td><</td><td>0.633</td>
<td>, 034</td><td><w [83]</td><td><</td><td>1,036</td><td>0614</td><td><</td><td>and [121]</td><td><</td><td>0616</td>
<td>, 032</td><td><in [84]</td><td><</td><td>1034</td><td>0.597</td><td><</td><td>and [122]</td><td><</td><td>0.599</td>
<td>.029</td><td><in [85]</td><td><</td><td>1.031</td><td>0.580</td><td><</td><td>and [123]</td><td><</td><td>0.582</td>
<td>, 025</td><td><w [86]</td><td><</td><td>1027</td><td>0563</td><td><</td><td>and [124]</td><td><</td><td>0.565</td>
<td>.021</td><td><w [87]</td><td><</td><td>1.023</td><td>0.546</td><td><</td><td>and [125]</td><td><</td><td>0.548</td>
<td>.016</td><td><in [88]</td><td><</td><td>1,018</td><td>0529</td><td><</td><td>and [126]</td><td><</td><td>0531</td>
<td>.011</td><td><w (89)</td><td><</td><td>1.013</td><td>0512</td><td><</td><td>and [127]</td><td><</td><td>0514</td>
<td>.005</td><td><in [9O)</td><td><</td><td>1.007</td><td>-0,497</td><td><</td><td>and [128]</td><td><</td><td>-0,495</td>
<td>.999</td><td><in [9l]</td><td><</td><td>1,001</td><td>-0,479</td><td><</td><td>and [129]</td><td><</td><td>-0,477</td>
<td>.992</td><td><w [92]</td><td><</td><td>0994</td><td>-0,462</td><td><</td><td>and [130]</td><td><</td><td>-0,460</td>
<td>.985</td><td><w [93]</td><td><</td><td>0.987</td><td>-0,445</td><td><</td><td>and [131]</td><td><</td><td>-0,443</td>
<td>.977</td><td><in [94]</td><td><</td><td>0979</td><td>-0,428</td><td><</td><td>and [132]</td><td><</td><td>-0,426</td>
<td>.969</td><td><w [95]</td><td><</td><td>0971</td><td>-0,411</td><td><</td><td>and [133]</td><td><</td><td>-0,409</td>
<td>.960</td><td><in [96]</td><td><</td><td>0.962</td><td>-0,394</td><td><</td><td>and [134]</td><td><</td><td>-0,392</td>
<td>.951</td><td><in [97]</td><td><</td><td>0.953</td><td>-0,377</td><td><</td><td>and [135]</td><td><</td><td>-0,375</td>
<td>.941</td><td><in [98]</td><td><</td><td>0.943</td><td>-0,360</td><td><</td><td>and [136]</td><td><</td><td>-0,358</td>
<td>.931</td><td><in [99]</td><td><</td><td>0933</td><td>-0,343</td><td><</td><td>and [137]</td><td><</td><td>-0,341</td>
<td>920</td><td><in [100]</td><td><</td><td>0922</td><td>-0,327</td><td><</td><td>w (138]</td><td><</td><td>-0,325</td>
<td>909</td><td><in [101]</td><td><</td><td>0911</td><td>-0,311</td><td><</td><td>w (139]</td><td><</td><td>-0,309</td>
<td>897</td><td><w (102)</td><td><</td><td>0899</td><td>-0,295</td><td><</td><td>and [140]</td><td><</td><td>-0,293</td>
<td>885</td><td><w [103]</td><td><</td><td>0887</td><td>-0,279</td><td><</td><td>and [141]</td><td><</td><td>-0,277</td>
<td>872</td><td><in [104]</td><td><</td><td>0.874</td><td>-0,263</td><td><</td><td>and [142]</td><td><</td><td>-0,261</td>
<td>860</td><td><in [105]</td><td><</td><td>0862</td><td>-0,248</td><td><</td><td>and [143]</td><td><</td><td>-0,246</td>
<td>846</td><td><in [106]</td><td><</td><td>0.848</td><td>-0,233</td><td><</td><td>and [144]</td><td><</td><td>-0,231</td>
<td>833</td><td><w [107]</td><td><</td><td>0.835</td><td>-0,218</td><td><</td><td>and [145]</td><td><</td><td>-0,216</td>
<td>819</td><td><w [108]</td><td><</td><td>0.821</td><td>-0,203</td><td><</td><td>and [146]</td><td><</td><td>-0,201</td>
<td>804</td><td><w [109]</td><td><</td><td>0806</td><td>-0,189</td><td><</td><td>and [147]</td><td><</td><td>-0,187</td>
<td>790</td><td><w [110]</td><td><</td><td>0792</td><td>-0,175</td><td><</td><td>and [148]</td><td><</td><td>-0,173</td>
<td>775</td><td><w [lll]</td><td><</td><td>0.777</td><td>-0,161</td><td><</td><td>and [149]</td><td><</td><td>-0,159</td>
<td>-0,147</td><td><</td><td>and [150]</td><td><</td><td>-0,145</td><td>0.125</td><td><</td><td>and [188]</td><td><</td><td>0.127</td>
<td>-0,134</td><td><</td><td>in [151]</td><td><</td><td>-0,132</td><td>• 0.126</td><td><</td><td>and [189]</td><td><</td><td>0.128</td>
<td>-0,121</td><td><</td><td>and [152]</td><td><</td><td>-0,119</td><td>0.126</td><td><</td><td>and [190]</td><td><</td><td>0.128</td>
<td>-0,108</td><td><</td><td>and [153]</td><td><</td><td>-0,106</td><td>0.126</td><td><</td><td>and [191]</td><td><</td><td>0.128</td>
<td>-0,096</td><td><</td><td>and [154]</td><td><</td><td>-0,094</td><td>0.126</td><td><</td><td>and [192]</td><td><</td><td>0.128</td>
<td>-0,084</td><td><</td><td>and [155]</td><td><</td><td>-0,082</td><td>0.127</td><td><</td><td>and [193]</td><td><</td><td>0.129</td>
<td>-0,072</td><td><</td><td>and [156)</td><td><</td><td>-0.070</td><td>0.126</td><td><</td><td>and [194]</td><td><</td><td>0.128</td>
<td>-0,061</td><td><</td><td>in (1571</td><td><</td><td>-0,059</td><td>0.126</td><td><</td><td>ii Γ1 Q51</td><td><</td><td>0.128</td>
<td></td><td></td><td>"L 'J</td><td></td><td></td><td></td><td></td><td>'' L <sup>χ</sup> J</td><td></td><td></td>
<td>-0.050</td><td><</td><td>and [158]</td><td><</td><td>-0,048</td><td>0.125</td><td><</td><td>and [196]</td><td><</td><td>0.127</td>
<td>-0,039</td><td><</td><td>and [159]</td><td><</td><td>-0,037</td><td>0.124</td><td><</td><td>and [197]</td><td><</td><td>0.126</td>
<td>-0,028</td><td><</td><td>and [160]</td><td><</td><td>-0,026</td><td>0.123</td><td><</td><td>and [198]</td><td><</td><td>0.125</td>
<td>-0,018</td><td><</td><td>and [161]</td><td><</td><td>-0,016</td><td>0.122</td><td><</td><td>in [199]</td><td><</td><td>0.124</td>
<td>-0,008</td><td><</td><td>and [162]</td><td><</td><td>-0,006</td><td>0.121</td><td><</td><td>and [200]</td><td><</td><td>0.123</td>
<td>0.001</td><td><</td><td>and [163]</td><td><</td><td>0.003</td><td>0.119</td><td><</td><td>and [201]</td><td><</td><td>0.121</td>
<td>0.010</td><td><</td><td>and [164J</td><td><</td><td>0012</td><td>0.118</td><td><</td><td>and [202]</td><td><</td><td>0.120</td>
<td>0.019</td><td><</td><td>and [165]</td><td><</td><td>0.021</td><td>0.116</td><td><</td><td>in [203]</td><td><</td><td>0.118</td>
<td>0.028</td><td><</td><td>and [166]</td><td><</td><td>0.030</td><td>'0.114</td><td><</td><td>and [204]</td><td><</td><td>0.116</td>
<td>0.036</td><td><</td><td>and [167]</td><td><</td><td>0.038</td><td>0.111</td><td><</td><td>and [205]</td><td><</td><td>0.113</td>
<td>0.043</td><td><</td><td>and [168]</td><td><</td><td>0.045</td><td>0.109</td><td><</td><td>and [206]</td><td><</td><td>0.111</td>
<td>0.051</td><td><</td><td>and [169]</td><td><</td><td>0.053</td><td>0.107</td><td><</td><td>and [2O7]</td><td><</td><td>0.109</td>
<td>0.058</td><td><</td><td>and [170]</td><td><</td><td>0.060</td><td>0.104</td><td><</td><td>in [208]</td><td><</td><td>0.106</td>
<td>0.065</td><td><</td><td>and [171]</td><td><</td><td>0.067</td><td>0.102</td><td><</td><td>in [209]</td><td><</td><td>0.104</td>
<td>0.071</td><td><</td><td>and [172]</td><td><</td><td>0.073</td><td>0.099</td><td><</td><td>in [210]</td><td><</td><td>0.101</td>
<td>0.077</td><td><</td><td>and [173]</td><td><</td><td>0.079</td><td>0.096</td><td><</td><td>and [211]</td><td><</td><td>0.098</td>
<td>0.082</td><td><</td><td>and [174]</td><td><</td><td>0.084</td><td>0.093</td><td><</td><td>and [212]</td><td><</td><td>0.095</td>
<td>0.088</td><td><</td><td>and [175]</td><td><</td><td>0.090</td><td>0.090</td><td><</td><td>and [213]</td><td><</td><td>0.092</td>
<td>0.093</td><td><</td><td>and [176]</td><td><</td><td>0.095</td><td>0.087</td><td><</td><td>and [214]</td><td><</td><td>0089</td>
<td>0.097</td><td><</td><td>and [177]</td><td><</td><td>0.099</td><td>0.084</td><td><</td><td>and [215]</td><td><</td><td>0.086</td>
<td>0.101</td><td><</td><td>and [178]</td><td><</td><td>0.103</td><td>0.082</td><td><</td><td>and [216]</td><td><</td><td>0.084</td>
<td>0.105</td><td><</td><td>and [179]</td><td><</td><td>0.107</td><td>0.079</td><td><</td><td>in [217]</td><td><</td><td>0.081</td>
<td>. 0.109</td><td><</td><td>and [180]</td><td><</td><td>0.111</td><td>0.076</td><td><</td><td>and [218]</td><td><</td><td>0.078</td>
<td>0.112</td><td><</td><td>and [181]</td><td><</td><td>0.114</td><td>0.073</td><td><</td><td>in [219]</td><td><</td><td>0.075</td>
<td>0.115</td><td><</td><td>and [182]</td><td><</td><td>0.117</td><td>0.070</td><td><</td><td>and [220]</td><td><</td><td>0.072</td>
<td>0.117</td><td><</td><td>and [183]</td><td><</td><td>0.119</td><td>0.067</td><td><</td><td>and [221]</td><td><</td><td>0.069</td>
<td>0.119</td><td><</td><td>and [184]</td><td><</td><td>0.121</td><td>0.064</td><td><</td><td>in [222]</td><td><</td><td>0.066</td>
<td>0.121</td><td><</td><td>and [185]</td><td><</td><td>0.123</td><td>* 0.061</td><td><</td><td>and [223]</td><td><</td><td>0.063</td>
<td>0.123</td><td><</td><td>and [186]</td><td><</td><td>0.125</td><td>0.058</td><td><</td><td>and [224]</td><td><</td><td>o: o6o</td>
<td>0.124</td><td><</td><td>and [187]</td><td><</td><td>0.126</td><td>0.055</td><td><</td><td>in [225]</td><td><</td><td>0.057</td>
<td>0.053 <</td><td>and [226]</td><td><</td><td>0.055</td><td>-0,006</td><td><</td><td>and [264]</td><td><</td><td>-0,004</td>
<td>0.050 <</td><td>and [227]</td><td><</td><td>0.052</td><td>-0,006</td><td><</td><td>and [265]</td><td><</td><td>-0,004</td>
<td>0.047 <</td><td>and [228]</td><td><</td><td>0.049</td><td>-0,005</td><td><</td><td>and [266]</td><td><</td><td>-0,003</td>
<td>0.045 <</td><td>and [229]</td><td><</td><td>0.047</td><td>-0,005</td><td><</td><td>in [267]</td><td><</td><td>-0,003</td>
<td>0.043 <</td><td>and [230]</td><td><</td><td>0.045 '</td><td>-0,005</td><td><</td><td>and [268]</td><td><</td><td>-0,003</td>
<td>0.040 <</td><td>and [231]</td><td><</td><td>0.042</td><td>-0,005</td><td><</td><td>and [269]</td><td><</td><td>-0,003</td>
<td>0.038 <</td><td>and [232]</td><td><</td><td>0.040</td><td>-0,004</td><td><</td><td>and [270)</td><td><</td><td>-0.002</td>
<td>0.036 <</td><td>and [233]</td><td><</td><td>0.038</td><td>-0,004</td><td><</td><td>w (271]</td><td><</td><td>-0.002</td>
<td>0.034 <</td><td>and [234]</td><td><</td><td>0.036</td><td>-0,004</td><td><</td><td>and [272]</td><td><</td><td>-0.002</td>
<td>0.032 <</td><td>and [235]</td><td><</td><td>0.034</td><td>-0,003</td><td><</td><td>and [273]</td><td><</td><td>-0,001</td>
<td>0.030 <</td><td>and [236]</td><td><</td><td>0.032</td><td>-0,003</td><td><</td><td>in [274]</td><td><</td><td>-0,001</td>
<td>0.028 <</td><td>and [237]</td><td><</td><td>0.030</td><td>-0,003</td><td><</td><td>and [275]</td><td><</td><td>-0,001</td>
<td>0.027 <</td><td>and [238]</td><td><</td><td>0.029</td><td>-0,003</td><td><</td><td>and [276]</td><td><</td><td>-0,001</td>
<td>0.025 <</td><td>and [239]</td><td><</td><td>0.027</td><td>-0.002</td><td><</td><td>and [277]</td><td><</td><td>0.000</td>
<td>0.023 <</td><td>and [240]</td><td><</td><td>0.025</td><td>-0.002</td><td><</td><td>and [278]</td><td><</td><td>0.000</td>
<td>0.022 <</td><td>and [241]</td><td><</td><td>0.024</td><td>-0.002</td><td><</td><td>and [279]</td><td><</td><td>0.000</td>
<td>0.021 <</td><td>and [242]</td><td><</td><td>0.023</td><td>-0.002</td><td><</td><td>and [280]</td><td><</td><td>0.000</td>
<td>0.019 <</td><td>and [243]</td><td><</td><td>0.021</td><td>-0.002</td><td><</td><td>and [281]</td><td><</td><td>0.000</td>
<td>0.018 <</td><td>and [244]</td><td><</td><td>0.020</td><td>-0.002</td><td><</td><td>and [282]</td><td><</td><td>0.000</td>
<td>0.017 <</td><td>and [245]</td><td><</td><td>0.019</td><td>-0,001</td><td><</td><td>and [283]</td><td><</td><td>0.001</td>
<td>0.016 <</td><td>and [246]</td><td><</td><td>0.018</td><td>-0,001</td><td><</td><td>and [284]</td><td><</td><td>0.001</td>
<td>0.015 <</td><td>and [247]</td><td><</td><td>0.017</td><td>-0,001</td><td><</td><td>and [285]</td><td><</td><td>0.001</td>
<td>0.014 <</td><td>and [248]</td><td><</td><td>0.016</td><td>-0,001</td><td><</td><td>and [286]</td><td><</td><td>0.001</td>
<td>0.013 <</td><td>and [249]</td><td><</td><td>0.015</td><td>0.000</td><td><</td><td>in [287]</td><td><</td><td>0.002</td>
<td>0.012 <</td><td>and [250]</td><td><</td><td>0.014</td><td>0.000</td><td><</td><td>and [288]</td><td><</td><td>0.002</td>
<td>0.011 <</td><td>and [251]</td><td><</td><td>0.013</td><td>0.000</td><td><</td><td>and [289]</td><td><</td><td>0.002</td>
<td>0.010 <</td><td>and [252]</td><td><</td><td>0012</td><td>0.000</td><td><</td><td>and [290]</td><td><</td><td>0.002</td>
<td>0.009 <</td><td>and [253]</td><td><</td><td>0011</td><td>0.000</td><td><</td><td>and [291]</td><td><</td><td>0.002</td>
<td>0.009 <</td><td>and [254]</td><td><</td><td>0011</td><td>0.001</td><td><</td><td>and [292]</td><td><</td><td>0.003</td>
<td>0.008 <</td><td>and [255]</td><td><</td><td>0.010</td><td>0.001</td><td><</td><td>in [293]</td><td><</td><td>0.003</td>
<td>-0.009 <</td><td>and [256]</td><td><</td><td>-0,007</td><td>0.001</td><td><</td><td>and [294]</td><td><</td><td>0.003</td>
<td>-0.009 <</td><td>and [257]</td><td><</td><td>-0,007</td><td>0.001</td><td><</td><td>and [295]</td><td><</td><td>0.003</td>
<td>-0.008 <</td><td>and [258]</td><td><</td><td>-0,006</td><td>0.000</td><td><</td><td>and [296]</td><td><</td><td>0.002</td>
<td>-0.008 <</td><td>and [259]</td><td><</td><td>-0,006</td><td>0.000</td><td><</td><td>and [297]</td><td><</td><td>0.002</td>
<td>-0.008 <</td><td>and [260]</td><td><</td><td>-0,006</td><td>0.000</td><td><</td><td>and [298]</td><td><</td><td>0.002</td>
<td>-0.007 <</td><td>and [261]</td><td><</td><td>-0,005</td><td>-0,001</td><td><</td><td>and [299]</td><td><</td><td>0.001</td>
<td>-0.007 <</td><td>and [262]</td><td><</td><td>-0,005</td><td>-0,001</td><td><</td><td>and [300]</td><td><</td><td>0.001</td>
<td>-0.006 <</td><td>and [263]</td><td><</td><td>-0,004</td><td>-0.002</td><td><</td><td>and [301]</td><td><</td><td>0.000</td>
<td>-0.002 <in [302]</td><td><0.000</td><td>0.000</td><td><w [340]</td><td><0.002</td>
<td>-0.003 <in [303]</td><td><-0.001</td><td>0.000</td><td><w [341]</td><td><0.002</td>
<td>-0.003 <in [304]</td><td><-0.001</td><td>0.000</td><td><in [342]</td><td><0.002</td>
<td>-0.004 <in [305]</td><td><-0.002</td><td>0.000</td><td><w [343]</td><td><0.002</td>
<td>-0.004 <w [306]</td><td><-0.002</td><td>-0,001</td><td><in [344]</td><td><0.001</td>
<td>-0.004 <in [307]</td><td><-0.002</td><td>-0,001</td><td><w [345]</td><td><0.001</td>
<td>-0.005 <in [308]</td><td><-0.003</td><td>0.000</td><td><w [346]</td><td><0.002</td>
<td>-0.005 <in [309]</td><td><-0.003</td><td>0.000</td><td><in [347]</td><td><0.002</td>
<td>-0.005 <in [310]</td><td><-0.003</td><td>0.001</td><td><w [348]</td><td><0.003</td>
<td>-0.006 <in [311]</td><td><-0.004</td><td>0.001</td><td><w [349]</td><td><0.003</td>
<td>-0.006 <in [312]</td><td><-0.004</td><td>0.001</td><td><w [350J</td><td><0.003</td>
<td>-0.006 <in [313]</td><td><-0.004</td><td>0.002</td><td><w [351]</td><td><0.004</td>
<td>-0.006 <in [314]</td><td><-0.004</td><td>0.002</td><td><w [352]</td><td><0.004</td>
<td>-0.006 <in [315]</td><td><-0.004</td><td>0.002</td><td><w [353]</td><td><0.004</td>
<td>-0.006 <in [316]</td><td><-0.004</td><td>0.002</td><td><w [354]</td><td><0.004</td>
<td>-0.005 <in [317]</td><td><-0.003</td><td>0.002</td><td><in [355]</td><td><0.004</td>
<td>-0.005 <in [318]</td><td><-0.003</td><td>0.001</td><td><w [356]</td><td><0.003</td>
<td>-0.005 <in [319]</td><td><-0.003</td><td>0.001</td><td><in [357]</td><td><0.003</td>
<td>-0.005 <w [320]</td><td><-0.003</td><td>0.001</td><td><w [358]</td><td><0.003</td>
<td>-0.004 <w [321]</td><td><-0.002</td><td>0.001</td><td><w [359]</td><td><0.003</td>
<td>-0.004 <w [322]</td><td><-0.002</td><td>0.001</td><td><in [360]</td><td><0.003</td>
<td>-0.004 <w [323]</td><td><-0.002</td><td>0.000</td><td><w [361]</td><td><0.002</td>
<td>-0.003 <w [324]</td><td><-0.001</td><td>0.000</td><td><w [362]</td><td><0.002</td>
<td>-0.003 <w [325]</td><td><-0.001</td><td>0.000</td><td><w [363]</td><td><0.002</td>
<td>-0.003 <w [326]</td><td><-0.001</td><td>-0,001</td><td><w [364]</td><td><0.001</td>
<td>-0.002 <w [327]</td><td><0.000</td><td>-0,001</td><td><in [365]</td><td><0.001</td>
<td>-0.002- <w [328]</td><td><0.000</td><td>-0,001</td><td><w [366]</td><td><0.001</td>
<td>-0.001 <w [329]</td><td><0.001</td><td>-0,001</td><td><w [367]</td><td><0.001</td>
<td>-0.001 <w [330]</td><td><0.001</td><td>-0.002</td><td><w [368]</td><td><0.000</td>
<td>-0.001 <w [331]</td><td><0.001</td><td>-0.002</td><td><w [369]</td><td><0.000</td>
<td>-0.001 <w [332]</td><td><0.001</td><td>-0.002</td><td><w [370]</td><td><0.000</td>
<td>-0.001 <w [333]</td><td><0.001</td><td>-0.002</td><td><in [371]</td><td><0.000</td>
<td>0.000 <in [334]</td><td><0.002</td><td>-0.002</td><td><in [372]</td><td><0.000</td>
<td>0.000 <in [335]</td><td><0.002</td><td>-0.002</td><td><in [373]</td><td><0.000</td>
<td>0.000 <in [336]</td><td><0.002</td><td>-0.002</td><td><in [374]</td><td><0.000</td>
<td>0.000 <in [337]</td><td><0.002</td><td>-0.002</td><td><w [375]</td><td><0.000</td>
<td>0.000 <in [338]</td><td><0.002</td><td>-0.002</td><td><in [376]</td><td><0.000</td>
<td>0.000 <in [339]</td><td><0.002</td><td>-0.002</td><td><in [377]</td><td><0.000</td>
-0.
-0.
-0.
-ο,
-ο,
-ο,
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
-ο
-ο
-ο
-ο
-ο
-ο
-ο
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<td>.002 <w [378] <0.000</td><td>-0,001</td><td><</td><td>and [416]</td><td><</td><td>0.001</td>
<td>.002 <w [379] <0.000</td><td>-0,001</td><td><</td><td>The [417]</td><td><</td><td>0.001</td>
<td>.002 <w [380] <0.000</td><td>-0,001</td><td><</td><td>and [418]</td><td><</td><td>0.001</td>
<td>.002 <w [381] <0.000</td><td>-0,001</td><td><</td><td>and [419]</td><td><</td><td>0.001</td>
<td>.002 <w [382] <0.000</td><td>-0,001</td><td><</td><td>and [420]</td><td><</td><td>0.001</td>
<td>.002 <w [383] <0.000</td><td>-0,001</td><td><</td><td>and [421]</td><td><</td><td>0.001</td>
<td>000 <in [384] <0.002</td><td>-0,001</td><td><</td><td>and [422]</td><td><</td><td>0.001</td>
<td>000 <w [385] <0.002</td><td>-0,001</td><td><</td><td>and [423]</td><td><</td><td>0.001</td>
<td>000 <w [386] <0.002</td><td>-0,001</td><td><</td><td>and [424]</td><td><</td><td>0.001</td>
<td>000 <in [387] <0.002</td><td>-0,001</td><td><</td><td>and [425]</td><td><</td><td>0.001</td>
<td>000 <w [388] <0.002</td><td>-0,001</td><td><</td><td>and [426]</td><td><</td><td>0.001</td>
<td>000 <w [389] <0.002</td><td>-0,001</td><td><</td><td>and [427]</td><td><</td><td>0.001</td>
<td>000 <w [390] <0.002</td><td>-0,001</td><td><</td><td>and [428]</td><td><</td><td>0.001</td>
<td>000 <in [391] <0.002</td><td>-0,001</td><td><</td><td>and [429]</td><td><</td><td>0.001</td>
<td>000 <in [392] <0.002</td><td>-0,001</td><td><</td><td>and [43O]</td><td><</td><td>0.001</td>
<td>000 <in [393] <0.002</td><td>-0,001</td><td><</td><td>and [431]</td><td><</td><td>0.001</td>
<td>.001 <w [394] <0.001</td><td>-0,001</td><td><</td><td>and [432]</td><td><</td><td>0.001</td>
<td>.001 <w [395] <0.001</td><td>-0,001</td><td><</td><td>and [433]</td><td><</td><td>0.001</td>
<td>.001 <w [396] <0.001</td><td>-0,001</td><td><</td><td>and [434]</td><td><</td><td>0.001</td>
<td>.001 <w [397] <0.001</td><td>-0,001</td><td><</td><td>and [435]</td><td><</td><td>0.001</td>
<td>.001 <w [398] <0.001</td><td>-0,001</td><td><</td><td>and [436]</td><td><</td><td>0.001</td>
<td>.001 <w [399] <0.001</td><td>-0,001</td><td><</td><td>and [437]</td><td><</td><td>0.001</td>
<td>.001 <w (400) <0.001</td><td>-0,001</td><td><</td><td>and [438]</td><td><</td><td>0.001</td>
<td>.001 <w [401] <0.001</td><td>-0,001</td><td><</td><td>and [439]</td><td><</td><td>0.001</td>
<td>.001 <w [402] <0.001</td><td>-0,001</td><td><</td><td>and [440]</td><td><</td><td>0.001</td>
<td>.001 <w [403] <0.001</td><td>-0001 '</td><td><</td><td>in [441]</td><td><</td><td>0.001</td>
<td>.001 <w [404] <0.001</td><td>-0,001</td><td><</td><td>and [442]</td><td><</td><td>0.001</td>
<td>.001 <w [405] <0.001</td><td>-0,001</td><td><</td><td>and [443]</td><td><</td><td>0.001</td>
<td>.001 <w [406] <0.001</td><td>-0,001</td><td><</td><td>and [444]</td><td><</td><td>0.001</td>
<td>.001 <w [4O7] <0.001</td><td>-0,001</td><td><</td><td>and [445]</td><td><</td><td>0.001</td>
<td>.001 <w [408] <0.001</td><td>-0,001</td><td><</td><td>and [446]</td><td><</td><td>0.001</td>
<td>.001 <w [409] <0.001 </td><td>-0,001</td><td><</td><td>and [447]</td><td><</td><td>0.001</td>
<td>.001 <w [410] <0.001</td><td>-0,001</td><td><</td><td>in [448]</td><td><</td><td>0.001</td>
<td>.001 <w [411] <0.001</td><td>-0,001</td><td><</td><td>and [449]</td><td><</td><td>0.001</td>
<td>.001 <w [412] <0.001</td><td>-0,001</td><td><</td><td>and [45O]</td><td><</td><td>Ο'.ΟΟΙ</td>
<td>.001 <w [413] <0.001</td><td>-0,001</td><td><</td><td>and [451]</td><td><</td><td>0.001</td>
<td>.001 <w [414] <0.001</td><td>-0,001</td><td><</td><td>and [452]</td><td><</td><td>0.001</td>
<td>.001 <w [415] <0.001</td><td>-0,001</td><td><</td><td>and [453]</td><td><</td><td>0.001</td>
<td>-0.001 <w [454)</td><td><0.001</td><td>-0.001 <w [492] <0.001</td>
<td>-0.001 <in [455]</td><td><0.001</td><td>-0.001 <w [493] <0.001</td>
<td>-0.001 <w [456]</td><td><0.001</td><td>-0.001 <w [494] <0.001</td>
<td>-0.001 <in [457]</td><td><0.001</td><td>-0.001 <w [495] <0.001</td>
<td>-0.001 <w [458]</td><td><0.001</td><td>-0.001 <w [496] <0.001</td>
<td>-0.001 <in [459]</td><td><0.001</td><td>-0.001 <w [497] <0.001</td>
<td>-0.001 <w [460]</td><td><0.001</td><td>-0.001 <w [498] <0.001</td>
<td>-0.001 <w [461]</td><td><0.001</td><td>-0.001 <w [499] <0.001</td>
<td>-0.001 <in [462]</td><td><0.001</td><td>-0.001 <w [500] <0.001</td>
<td>-0.001 <w [463]</td><td><0.001</td><td>-0.001 <w [501] <0.001</td>
<td>-0.001 <w [464]</td><td><0.001</td><td>-0.001 <w [502] <0.001</td>
<td>-0.001 <w [465]</td><td><0.001</td><td>-0.001 <w [503] <0.001</td>
<td>-0.001 <w [466]</td><td><0.001</td><td>-0.001 <w [504] <0.001</td>
<td>-0.001 <w [467]</td><td><0.001</td><td>-0.001 <w [505] <0.001</td>
<td>-0.001 <w [468]</td><td><0.001</td><td>-0.001 <w [506] <0.001</td>
<td>-0.001 <w (469)</td><td><0.001</td><td>-0.001 <w [507] <0.001</td>
<td>-0.001 <w [470]</td><td><0.001</td><td>-0.001 <w [508] <0.001</td>
<td>-0.001 <in [471]</td><td><0.001</td><td>-0.001 <w [509] <0.001</td>
<td>-0.001 <in [472]</td><td><0.001</td><td>-0.001 <w [510] <0.001</td>
<td>-0.001 <in [473]</td><td><0.001</td><td>-0.001 <w [511] <0.001</td>
<td>-0.001 <in [474]</td><td><0.001</td><td>-0.001 <w [512] <0.001</td>
<td>-0.001 <w [475]</td><td><0.001</td><td>• -0.001 <w [513] <0.001</td>
<td>-0.001 <in [476]</td><td><0.001</td><td>-0.001 <w [514] <0.001</td>
<td>-0.001 <w [477]</td><td><0.001</td><td>-0.001 <w [515] <0.001</td>
<td>-0.001 <w [478]</td><td><0.001</td><td>-0.001 <w [516] <0.001</td>
<td>0.000 <in [479]</td><td><0.002</td><td>-0.001 <w [517] <0.001</td>
<td>-0.001 <w [480]</td><td><0.001</td><td>-0.001 <.w [518] <0.001</td>
<td>-0.001 <in [481]</td><td><0.001</td><td>-0.001 <w [519] <0.001</td>
<td>-0.001 <in [482]</td><td><0.001</td><td>-0.001 <w [520] <0.001</td>
<td>-0.001 <in [483]</td><td><0.001</td><td>-0.001 <w [521] <0.001</td>
<td>-0.001 <w [484]</td><td><0.001</td><td>-0.001 <w [522] <0.001</td>
<td>-0.001 <w [485]</td><td><0.001</td><td>-0.001 <w [523] <0.001</td>
<td>-0.001 <w [486]</td><td><0.001</td><td>-0.001 <w [524] <0.001</td>
<td>-0.001 <in [487]</td><td><0.001</td><td>-0.001 <w [525] <0.001</td>
<td>-0.001 <w [488]</td><td><0.001</td><td>-0.001 <w [526] <0.001</td>
<td>-0.001 <in [489]</td><td><0.001</td><td>-0.001 <w [527] <0.001</td>
<td>-0.001 <w [490]</td><td><0.001</td><td>-0.001 <w [528] <0.001</td>
<td>-0.001 <in [491]</td><td><0.001</td><td>-0.001 <w [529] <0.001</td>
<td>-0.001 <w [530]</td><td><0.001</td><td>-0,001</td><td><w [568]</td><td><0.001</td>
<td>-0.001 <w [531]</td><td><0.001.</td><td>-0,001</td><td><in [569]</td><td><0.001</td>
<td>-0.001 <w [532]</td><td><0.001</td><td>-0,001</td><td><in [570]</td><td><0.001</td>
<td>-0.001 <w [533]</td><td><0.001</td><td>-0,001</td><td><w [571]</td><td><0.001</td>
<td>-0.001 <w [534]</td><td><0.001</td><td>-0,001</td><td><w [572]</td><td><0.001</td>
<td>-0.001 <w [535]</td><td><0.001</td><td>-0,001</td><td><w [573]</td><td><0.001</td>
<td>-0.001 <w [536]</td><td><0.001</td><td>-0,001</td><td><w [574]</td><td><0.001</td>
<td>-0.001 <w [537]</td><td><0.001</td><td>-0,001</td><td><in [575]</td><td><0.001</td>
<td>-0.001 <w [538]</td><td><0.001</td><td>-0,001</td><td><w [576]</td><td><0.001</td>
<td>-0.001 <in [539]</td><td><0.001</td><td>-0,001</td><td><w [577]</td><td><0.001</td>
<td>-0.001 <w [540]</td><td><0.001</td><td>-0,001</td><td><w [578]</td><td><0.001</td>
<td>-0.001 <w [541]</td><td><0.001</td><td>-0,001</td><td><w [579]</td><td><0.001</td>
<td>-0.001 <w [542]</td><td><0.001</td><td>-0,001</td><td><w [580]</td><td><0.001</td>
<td>-0.001 <w [543]</td><td><0.001</td><td>-0,001</td><td><w [581]</td><td><0.001</td>
<td>-0.001 <w [544]</td><td><0.001</td><td>-0,001</td><td><w [582]</td><td><0.001</td>
<td>-0.001 <w [545]</td><td><0.001</td><td>-0,001</td><td><w [583]</td><td><0.001</td>
<td>-0.001 <w [546]</td><td><0.001</td><td>-0,001</td><td><w [584]</td><td><0.001</td>
<td>-0.001 <w [547]</td><td><0.001</td><td>-0,001</td><td><w [585]</td><td><0.001</td>
<td>-0.001 <w [548]</td><td><0.001</td><td>-0,001</td><td><w [586]</td><td><0.001</td>
<td>-0.001 <w [549]</td><td><0.001</td><td>-0,001</td><td><w [587]</td><td><0.001</td>
<td>-0.001 <w [550]</td><td><0.001</td><td>-0,001</td><td><in [588]</td><td><0.001</td>
<td>-0.001 <in [551]</td><td><0.001</td><td>-0,001</td><td><w [589]</td><td><0.001</td>
<td>-0.001 <w [552]</td><td><0.001</td><td>-0,001</td><td><in [59O]</td><td><0.001</td>
<td>-0.001 <w [553]</td><td><0.001</td><td>'-0.001</td><td><in [591]</td><td><0.001</td>
<td>-0.001 <w [554]</td><td><0.001</td><td>-0,001</td><td><in [592]</td><td><0.001</td>
<td>-0.001 <w [555]</td><td><0.001</td><td>-0,001</td><td><in [593]</td><td><0.001</td>
<td>-0.001 <w [556]</td><td><0.001</td><td>-0,001</td><td><in [594]</td><td><0.001</td>
<td>-0.001 <w [557]</td><td><0.001</td><td>-0,001</td><td><w [595]</td><td><0.001</td>
<td>-0.001 <w [558]</td><td><0.001</td><td>-0,001</td><td><in [596]</td><td><0.001</td>
<td>-0.001 <in [5.59]</td><td><0.001</td><td>-0,001</td><td><w [597]</td><td><0.001</td>
<td>-0.001 <w [560]</td><td><0.001</td><td>-0,001</td><td><in [598]</td><td><0.001</td>
<td>-0.001 <in [561]</td><td><0.001</td><td>-0,001</td><td><in [599]</td><td><0.001</td>
<td>-0.001 <in [562]</td><td><0.001</td><td>-0,001</td><td><in [600]</td><td><0.001</td>
<td>-0.001 <in [563]</td><td><0.001</td><td>-0,001</td><td><in [601]</td><td><0.001</td>
<td>-0.001 <w [564]</td><td><0.001</td><td>-0,001</td><td><in [602]</td><td><0.001</td>
<td>-0.001 <w [565]</td><td><0.001</td><td>-0,001</td><td><in [603]</td><td><0.001</td>
<td>-0.001 <w [566]</td><td><0.001</td><td>-0,001</td><td><in [604]</td><td><0.001</td>
<td>-0.001 <w [567]</td><td><0.001</td><td>-0,001</td><td><w (605)</td><td><0.001</td>
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0,001
-0.001 <w [606] <w [607] <w [608] <w [609] <w [610] <w [611] <w [612] <w [613] <w [614] <w [ [617] <w (616) 625] <w [626] <w [627] <w [628] <w [629] <w [630] <w [631] <w [632] <w [633] <w [634] <w [ 635] <w [636] <w [637] <w [638] <w [639] <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001 <0.001
<td>Annex 4</td><td></td><td></td><td></td><td></td><td></td><td>. 0.592</td><td><</td><td>1 in [36]</td><td>| <</td><td>0.594</td>
<td></td><td></td><td></td><td></td><td></td><td></td><td>0.609</td><td><</td><td>1 in [37]</td><td>| <</td><td>0611</td>
<td>0.010</td><td><</td><td>a [0]</td><td>1</td><td><</td><td>0012</td><td>0.625</td><td><</td><td>1 in [38]</td><td>| <</td><td>0.627</td>
<td>0.023</td><td><</td><td>W [L]</td><td>1</td><td><</td><td>0.025</td><td>0.642</td><td><</td><td>1 in [39]</td><td>| <</td><td>0.644</td>
<td>0.034</td><td><</td><td>W [2]</td><td>1</td><td><</td><td>0.036</td><td>0.658</td><td><</td><td>1 in [40]</td><td>I <</td><td>0.660</td>
<td>0.045</td><td><</td><td>in [3]</td><td>1</td><td><</td><td>0.047</td><td>0674</td><td><</td><td>1 in [41]</td><td>I <</td><td>0.676</td>
<td>0.058</td><td><</td><td>in [4]</td><td>1</td><td><</td><td>0.060</td><td>0.690</td><td><</td><td>1 in [42]</td><td>I <</td><td>0692</td>
<td>0.072</td><td><</td><td>and [5]</td><td>1</td><td><</td><td>0.074</td><td>0.706</td><td><</td><td>1 in [43]</td><td>I <</td><td>0.708</td>
<td>0.087</td><td><</td><td>in [6]</td><td>1</td><td><</td><td>0089</td><td>0722</td><td><</td><td>1 in [44]</td><td>| <</td><td>0.724</td>
<td>0.103</td><td><I</td><td>in [7]</td><td>1</td><td><</td><td>0.105</td><td>0738</td><td><</td><td>1 in [45]</td><td>| <</td><td>0740</td>
<td>0.120</td><td><</td><td>in [8]</td><td>1</td><td><</td><td>0.122</td><td>0753</td><td><</td><td>1 in [46]</td><td>| <</td><td>0755</td>
<td>0.137</td><td><</td><td>in [9]</td><td>1</td><td><</td><td>0.139</td><td>0.769</td><td><</td><td>1 in [47]</td><td>I <</td><td>0.771</td>
<td>0.154</td><td><1</td><td>in [10]</td><td></td><td><</td><td>0.156</td><td>0.784</td><td><</td><td>| and [48]</td><td>I <</td><td>0786</td>
<td>0.171</td><td><1</td><td>in [ll]</td><td>1</td><td><</td><td>0.173</td><td>0.799</td><td><</td><td>1 in [49]</td><td>I <</td><td>0801</td>
<td>0.188</td><td><1</td><td>and [12]</td><td>1</td><td><</td><td>0.190</td><td>0.815</td><td><</td><td>1 in [50]</td><td>I <</td><td>0817</td>
<td>0.205</td><td><|</td><td>and [13]</td><td>1</td><td><</td><td>0.207</td><td>0.830</td><td><</td><td>1 in [51]</td><td>| <</td><td>0832</td>
<td>0.222</td><td><1</td><td>in [14]</td><td>1</td><td><</td><td>0.224</td><td>0.845</td><td><</td><td>1 in [52]</td><td>| <</td><td>0847</td>
<td>0.239</td><td><|</td><td>and [15]</td><td>1</td><td><</td><td>0.241</td><td>0.860</td><td><</td><td>1 in [53]</td><td>I <</td><td>0862</td>
<td>0.256</td><td><|</td><td>in [16]</td><td>1</td><td><</td><td>0.258</td><td>0.874</td><td><</td><td>1 in [54]</td><td>I <</td><td>0876</td>
<td>0.272</td><td><1</td><td>and [17]</td><td>1</td><td><</td><td>0.274</td><td>0.889</td><td><</td><td>1 in [55]</td><td>| <</td><td>0891</td>
<td>0.289</td><td><1</td><td>and [18]</td><td>1</td><td><</td><td>0.291</td><td> 0.903</td><td><</td><td>1 in [56]</td><td>| <</td><td>0.905</td>
<td>0.306</td><td><1</td><td>and [19]</td><td>1</td><td><</td><td>0.308</td><td>0917</td><td><</td><td>1 in [57]</td><td>I <</td><td>0.919</td>
<td>0323</td><td><1</td><td>and [20]</td><td>1</td><td><</td><td>0.325</td><td>0.930</td><td><</td><td>1 in [58]</td><td>| <</td><td>0.932</td>
<td>0.339</td><td><1</td><td>and [21]</td><td>1</td><td><</td><td>0.341</td><td>0.943</td><td><</td><td>1 in [59]</td><td>I <</td><td>0945</td>
<td>0.356</td><td><|</td><td>and [22]</td><td>1</td><td><</td><td>0358</td><td>0956</td><td><</td><td>1 in [60]</td><td>I <</td><td>0958</td>
<td>0.373</td><td><|</td><td>and [23]</td><td>1</td><td><</td><td>0.375</td><td>0.968</td><td><</td><td>1 in [61]</td><td>| <</td><td>0.970</td>
<td>'0.390</td><td><|</td><td>in [24]</td><td>1</td><td><</td><td>0.392</td><td>0980</td><td><</td><td>1 in [62]</td><td>| <</td><td>0.982</td>
<td>0.407</td><td><|</td><td>and [25]</td><td>1</td><td><</td><td>0.409</td><td>0.992</td><td><</td><td>and [63]</td><td>I <</td><td>0994</td>
<td>0.424</td><td><|</td><td>and [26]</td><td>1</td><td><</td><td>0.426</td><td>1,000</td><td><</td><td>And in [64]</td><td>I <</td><td>1.002</td>
<td>0441</td><td><1</td><td>and [27]</td><td>1</td><td><</td><td>0443</td><td>1006</td><td><</td><td>1 in [65]</td><td>| <</td><td>1008</td>
<td>0.458</td><td><1</td><td>in [28]</td><td>1</td><td><</td><td>0.460</td><td>1,012</td><td><</td><td>1 in [66]</td><td>I <</td><td>1.014</td>
<td>0.475</td><td><1</td><td>and [29]</td><td>1</td><td><</td><td>0477</td><td>1,017</td><td><</td><td>1 in [67]</td><td>| <</td><td>1,019</td>
<td>0.492</td><td><1</td><td>and [30]</td><td>1</td><td><</td><td>0.494</td><td>1,021</td><td><</td><td>And in [68]</td><td>| <</td><td>1.023</td>
<td>0.509</td><td><|</td><td>and [31]</td><td>1</td><td><</td><td>0.511</td><td>1,026</td><td><</td><td>1 in [69]</td><td>I <</td><td>1.028</td>
<td>0525</td><td><|</td><td>and [32]</td><td>1</td><td><</td><td>0527</td><td>1.029</td><td><</td><td>1 in [70]</td><td>| <</td><td>1.031</td>
<td>0542</td><td><1</td><td>and [33]</td><td>1</td><td><</td><td>0544</td><td>1,032</td><td><</td><td>1 in [71]</td><td>I <</td><td>1034</td>
<td>0.559</td><td><1</td><td>in (34]</td><td>1</td><td><</td><td>0.561</td><td>1.035</td><td><</td><td>1 in [72]</td><td>I <</td><td>1.037</td>
<td>0.575</td><td><1</td><td>and [35]</td><td>1</td><td><</td><td>0.577</td><td>1.037</td><td><</td><td>1 in [73]</td><td>I <</td><td>1.039</td>
100
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
1.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
<td>038 <</td><td colspan="2">1 in [74] 1</td><td><1.040</td><td>0.760</td><td><</td><td colspan="2">1 in [112]</td><td colspan="2">| <</td><td>0.762</td>
<td>039 <</td><td>1</td><td>in [75] 1</td><td><1.041</td><td>0745</td><td><</td><td>1</td><td>and [113]</td><td>1</td><td><</td><td>0.747</td>
<td>040 <</td><td>1</td><td>in [76]</td><td><1.042</td><td>0729</td><td><</td><td>1</td><td>in [114].</td><td>1</td><td><</td><td>0731</td>
<td>040 <</td><td>1</td><td>In [77]</td><td><1.042</td><td>0.713</td><td><</td><td>1</td><td>and [115]</td><td>1</td><td><</td><td>0.715</td>
<td>040 <</td><td>1</td><td>in [78]</td><td><1,042</td><td>0.697</td><td><</td><td>1</td><td>and [116]</td><td>1</td><td><</td><td>0699</td>
<td>040 <</td><td>1</td><td>in [79]</td><td><1.042</td><td>0.681</td><td><</td><td>1</td><td>and [117]</td><td>1</td><td><</td><td>0683</td>
<td>039 <</td><td>1</td><td>in [80] |</td><td><1.041</td><td>0664</td><td><</td><td>1</td><td>and [118]</td><td>1</td><td><</td><td>0666</td>
<td>038 <</td><td>1</td><td>in [81]</td><td><1.040</td><td>0648</td><td><</td><td>1</td><td>and [119]</td><td>1</td><td><</td><td>0.650</td>
<td>036 <</td><td>1</td><td>in [82]</td><td><1.038</td><td>. 0631</td><td><</td><td>1</td><td>and [120]</td><td>1</td><td><</td><td>0.633</td>
<td>034 <</td><td>1</td><td>in [83]</td><td><1.036</td><td>0614</td><td><</td><td>1</td><td>and [121]</td><td>1</td><td><</td><td>0616</td>
<td>032 <</td><td>1</td><td>in [84]</td><td><1.034</td><td>0.597</td><td><</td><td>1</td><td>and [122]</td><td>1</td><td><</td><td>0.599</td>
<td>029 <</td><td>1</td><td>in [85]</td><td><1.031</td><td>0.580</td><td><</td><td>1</td><td>and [123]</td><td>1</td><td><</td><td>0.582</td>
<td>025 <</td><td>1</td><td>in [86] 1</td><td><1.027</td><td>0563</td><td><</td><td>1</td><td>and [124]</td><td>1</td><td><</td><td>0.565</td>
<td>021 <</td><td>1</td><td>in [87]</td><td><1.023</td><td>0.546</td><td><</td><td>1</td><td>and [125]</td><td>1</td><td><</td><td>0.548</td>
<td>016 <</td><td>1</td><td>in [88] 1</td><td><1.018</td><td>0529</td><td><</td><td></td><td>and [126]</td><td>1</td><td><</td><td>0531</td>
<td>011 <</td><td>1</td><td>in [89] 1</td><td><1.013</td><td>0512</td><td><</td><td>1</td><td>and [127]</td><td>1</td><td><</td><td>0514</td>
<td>005 <</td><td></td><td>in [90] 1</td><td><1.007</td><td>0.495</td><td><</td><td>1</td><td>and [128]</td><td>1</td><td><</td><td>0.497</td>
<td>999 <</td><td>1</td><td>in [91] 1</td><td><1.001</td><td>0477</td><td><</td><td>1</td><td>and [129]</td><td>1</td><td><</td><td>0.479</td>
<td>992 <</td><td>1</td><td>in [92]</td><td><0.994</td><td>0.460</td><td><</td><td></td><td>and [130]</td><td>1</td><td><</td><td>0.4 62</td>
<td>985 <</td><td>1</td><td>in [93] 1</td><td><0.987</td><td>0443</td><td><</td><td>1</td><td>and [131]</td><td>1</td><td><</td><td>0445</td>
<td>.977 <</td><td>1</td><td>in [94] 1</td><td><0979</td><td>0.426</td><td><</td><td>1</td><td>and [132]</td><td>1</td><td><</td><td>0.428</td>
<td>.969 <</td><td></td><td>in [95] 1</td><td><0.971</td><td>0.409</td><td><</td><td>1</td><td>and [133]</td><td>1</td><td><</td><td>0.411</td>
<td>.960 <</td><td>1</td><td>in [96] 1</td><td><0.962</td><td>0.392</td><td><</td><td></td><td>and [134]</td><td>1</td><td><</td><td>0.394</td>
<td>.951 <</td><td>1</td><td>in [97] 1</td><td><0.953</td><td>0.375</td><td><</td><td>1</td><td>and [135]</td><td>1</td><td><</td><td>0377</td>
<td>.941 <</td><td>1</td><td>in [98]</td><td><0.943</td><td>0358</td><td><</td><td>1</td><td>and [136]</td><td>1</td><td><</td><td>0.360</td>
<td>.931 <</td><td>1</td><td>in [99] 1</td><td><0.933</td><td>0.341</td><td><</td><td>1</td><td>and [137]</td><td>1</td><td><</td><td>0.343</td>
<td>920 <</td><td></td><td>in [100] 1</td><td><0.922</td><td>0.325</td><td><</td><td>1</td><td>and [138]</td><td>1</td><td><</td><td>0.327</td>
<td>909 <</td><td>1</td><td>and [101]</td><td><0.911</td><td>0.309</td><td><</td><td>1</td><td>and [139]</td><td>1</td><td><</td><td>0.311</td>
<td>897 <</td><td>1</td><td>and [102]</td><td><0.899</td><td>0.293</td><td><</td><td>1</td><td>and [140]</td><td>1</td><td><</td><td>0.295</td>
<td>885 <</td><td>1</td><td>and [103]</td><td><0.887</td><td>0.277</td><td><</td><td>1</td><td>and [141]</td><td>1</td><td><</td><td>0.279</td>
<td>872 <</td><td>1</td><td>and [104]</td><td><0.874</td><td>0261</td><td><</td><td>1</td><td>and [142]</td><td>1</td><td><</td><td>0.263</td>
<td>860 <</td><td>1</td><td>and [105]</td><td><0.862</td><td>0.246</td><td><</td><td>1</td><td>and [143]</td><td>1</td><td><</td><td>0.248</td>
<td>846 <</td><td>1</td><td>and [106]</td><td><0.848</td><td>0.231</td><td><</td><td>1</td><td>and [144]</td><td>1</td><td><</td><td>0.233</td>
<td>833 <</td><td>1</td><td>and [107]</td><td><0.835</td><td>0216</td><td><</td><td>1</td><td>and [145]</td><td>1</td><td><</td><td>0.218</td>
<td>819 <</td><td>1</td><td>and [108]</td><td><0.821</td><td>0.201</td><td><</td><td>1</td><td>and [146]</td><td>1</td><td><</td><td>0.203</td>
<td>804 <</td><td>1</td><td>and [109)</td><td><0.806</td><td>0.187</td><td><</td><td>1</td><td>and [147]</td><td>1</td><td><</td><td>0.189</td>
<td>790 <</td><td>1</td><td>and [110]</td><td><0.792</td><td>0.173</td><td><</td><td>1</td><td>and [148]</td><td></td><td><</td><td>0.175</td>
<td>775 <</td><td>1</td><td>and [III]</td><td><0.777</td><td>0.159</td><td><</td><td>1</td><td>and [149]</td><td>1</td><td><</td><td>0.161</td>
101
<td>0.145</td><td><</td><td>1</td><td>and [150]</td><td>1</td><td><</td><td>0.147</td><td>0.125</td><td><</td><td>1</td><td>and [188]</td><td>1</td><td><</td><td>0.127</td>
<td>0.132</td><td><</td><td>1</td><td>and [151]</td><td>1</td><td><</td><td>0.134</td><td>0.126</td><td><</td><td>1</td><td>and [189]</td><td>1</td><td><</td><td>0128 ·</td>
<td>0.119</td><td><</td><td>1</td><td>and [152]</td><td>1</td><td><</td><td>0.121</td><td>0.126</td><td><</td><td>1</td><td>and [190]</td><td>1</td><td><</td><td>0.128</td>
<td>0.106</td><td><</td><td>1</td><td>in [153J</td><td>1</td><td><</td><td>0.108</td><td>0.126</td><td><</td><td>1</td><td>and [191]</td><td>1</td><td><</td><td>0.128</td>
<td>0.094</td><td><</td><td>1</td><td>and [154]</td><td>1</td><td><</td><td>0.096</td><td>0.126</td><td><</td><td>1</td><td>in [192]</td><td>1</td><td><</td><td>0.128</td>
<td>0.082</td><td><</td><td>1</td><td>and [155]</td><td>1</td><td><</td><td>0.084</td><td>0.127</td><td><</td><td>1</td><td>and [193]</td><td>1</td><td><</td><td>0.129</td>
<td>0.070</td><td><</td><td>1</td><td>and [156]</td><td>1</td><td><</td><td>0.072</td><td>0.126</td><td><</td><td>1</td><td>and [194]</td><td></td><td><</td><td>0.128</td>
<td>λ ης</td><td>X</td><td>1</td><td>... (1 £ Tl</td><td></td><td>X</td><td>n nci</td><td>Λ 1OC</td><td>X</td><td>L</td><td>T., f1</td><td></td><td>X</td><td>Λ 1 OO</td>
<td>V · V -> -></td><td>χ</td><td>1</td><td>W [1J / j</td><td></td><td>X</td><td>\ J. UU and</td><td>W · J. £. AT</td><td>X</td><td>1</td><td>in L ± j</td><td></td><td>X</td><td>U. 1. U.</td>
<td>0.048</td><td><</td><td>1</td><td>and [158]</td><td>1</td><td><</td><td>0.050</td><td>0.125</td><td><</td><td>1</td><td>and [196]</td><td>1</td><td><</td><td>0.127</td>
<td>0.037</td><td><</td><td>1</td><td>and [159]</td><td>1</td><td><</td><td>0.039</td><td>0.124</td><td><</td><td>1</td><td>and [197]</td><td>1</td><td><</td><td>0.126</td>
<td>0.026</td><td><</td><td>1</td><td>and [160]</td><td>1</td><td><</td><td>0.028</td><td>0.123</td><td><</td><td>1</td><td>in [198]</td><td>1</td><td><</td><td>0.125</td>
<td>0.016</td><td><</td><td>1</td><td>and [161]</td><td>1</td><td><</td><td>0.018</td><td>0.122</td><td><</td><td>1</td><td>and [199]</td><td>1</td><td><</td><td>0.124</td>
<td>0.006</td><td><</td><td>1</td><td>and [162]</td><td>1</td><td><</td><td>0.008</td><td>0.121</td><td><</td><td>1</td><td>and [200]</td><td>1</td><td><</td><td>0.123</td>
<td>0.001</td><td><</td><td>1</td><td>and [163]</td><td>1</td><td><</td><td>0.003</td><td>0.119</td><td><</td><td>1</td><td>and [201]</td><td>1</td><td><</td><td>0.121</td>
<td>0.010</td><td><</td><td>1</td><td>and [164]</td><td>1</td><td><</td><td>0012</td><td>0.118</td><td><</td><td>1</td><td>and [202]</td><td>1</td><td><</td><td>0.120</td>
<td>0.019</td><td><</td><td>1</td><td>in [165]</td><td>1</td><td><</td><td>0.021</td><td>0.116</td><td><</td><td>1</td><td>and [203]</td><td>1</td><td><</td><td>0.118</td>
<td>0.028</td><td><</td><td>1</td><td>and [166]</td><td>1</td><td><</td><td>0.030</td><td>0.114</td><td><</td><td>1</td><td>and [204]</td><td>1</td><td><</td><td>0.116</td>
<td>0.036</td><td><</td><td>1</td><td>and [167]</td><td>1</td><td><</td><td>0.038</td><td>0.111</td><td><</td><td>1</td><td>and [205]</td><td>1</td><td><</td><td>0.113</td>
<td>0.043</td><td><</td><td>1</td><td>and [168]</td><td>1</td><td><</td><td>0.045</td><td>0.109</td><td><</td><td>1</td><td>and [206]</td><td>1</td><td><</td><td>0.111</td>
<td>0.051</td><td><</td><td>1</td><td>and [169]</td><td>1</td><td><</td><td>0.053</td><td>0.107</td><td><</td><td>1</td><td>and [207]</td><td>1</td><td><</td><td>0.109</td>
<td>0.058</td><td><</td><td>1</td><td>and [170]</td><td>1</td><td><</td><td>0.060</td><td>0.104</td><td><</td><td>1</td><td>in [208]</td><td>1</td><td><</td><td>0.106</td>
<td>0.065</td><td><</td><td>1</td><td>and [171]</td><td>1</td><td><</td><td>0.067</td><td>0.102</td><td><</td><td>1</td><td>and [209]</td><td>1</td><td><</td><td>0.104</td>
<td>0.071</td><td><</td><td>1</td><td>and [172)</td><td>1</td><td><</td><td>0.073</td><td>0.099</td><td><</td><td>1</td><td>and [210]</td><td>1</td><td><</td><td>0.101</td>
<td>0.077</td><td><</td><td>1</td><td>and [173] ·</td><td>1</td><td><</td><td>0.079</td><td>0.096</td><td><</td><td>1</td><td>and [211]</td><td>1</td><td><</td><td>0.098</td>
<td>0.082</td><td><</td><td>1</td><td>and [174]</td><td>1</td><td><</td><td>0.084</td><td>0.093</td><td><</td><td>1</td><td>and [212]</td><td>1</td><td><</td><td>0.095</td>
<td>0.088</td><td><</td><td>1</td><td>and [175]</td><td>1</td><td><</td><td>0.090</td><td>0.090</td><td><</td><td>1</td><td>and [213]</td><td>1</td><td><</td><td>0.092</td>
<td>0.093</td><td><</td><td>1</td><td>and [176]</td><td>1</td><td><</td><td>0.095</td><td>0.087</td><td><</td><td>1</td><td>and [214]</td><td>1</td><td><</td><td>0089</td>
<td>0.097</td><td><</td><td>1</td><td>and [177]</td><td>1</td><td><</td><td>0.099</td><td>0.084</td><td><</td><td>1</td><td>and [215]</td><td>1</td><td><</td><td>0.086</td>
<td>0.101</td><td><</td><td>1</td><td>in [178]</td><td>1</td><td><</td><td>0.103</td><td>0.082</td><td><</td><td>1</td><td>and [216]</td><td>1</td><td><</td><td>0.084</td>
<td>0.105</td><td><</td><td>1</td><td>and [179]</td><td>1</td><td><</td><td>0.107</td><td>0.079</td><td><</td><td>1</td><td>and [217]</td><td>1</td><td><</td><td>0.081</td>
<td>0.109</td><td><</td><td>1</td><td>and [180]</td><td>1</td><td><</td><td>0.111</td><td>0.076</td><td><</td><td>1</td><td>and [218)</td><td></td><td><</td><td>0.078</td>
<td>0.112</td><td><</td><td>1</td><td>and [181]</td><td>1</td><td><</td><td>0.114</td><td>0.073</td><td><</td><td>1</td><td>and [219)</td><td>1</td><td><</td><td>0.075</td>
<td>0.115</td><td><</td><td>1</td><td>and [182]</td><td>1</td><td><</td><td>0.117</td><td>0.070</td><td><</td><td>1</td><td>and [220]</td><td>1</td><td><</td><td>0.072</td>
<td>0.117</td><td><</td><td>1</td><td>and [183]</td><td>1</td><td><</td><td>0.119</td><td>. 0.067</td><td><</td><td>1</td><td>w (221]</td><td>1</td><td><</td><td>0.069</td>
<td>0.119</td><td><</td><td>1</td><td>and [184]</td><td>1</td><td><</td><td>0.121</td><td>0.064</td><td><</td><td>1</td><td>and [222]</td><td>1</td><td><</td><td>0.066</td>
<td>0.121</td><td><</td><td>1</td><td>and [185]</td><td>1</td><td><</td><td>0.123</td><td>0.061</td><td><</td><td>1</td><td>and [223]</td><td>1</td><td><</td><td>0.063</td>
<td>0.123</td><td><</td><td>1</td><td>and [186]</td><td>1</td><td><</td><td>0.125</td><td>0.058</td><td><</td><td>1</td><td>and [224]</td><td>1</td><td><</td><td>0.060</td>
<td>0.124</td><td><</td><td>1</td><td>and [187]</td><td>1</td><td><</td><td>0.126</td><td>0.055</td><td><</td><td>1</td><td>and [225]</td><td>1</td><td><</td><td>0.057</td>
102
<td>0.053 <</td><td>1 in [226]</td><td>| <</td><td>0.055</td><td>0.004 <</td><td>1 in [264]</td><td>1 <0.006</td>
<td>0.050. <</td><td>1 in [227]</td><td>| <</td><td>0.052</td><td>0.004 <</td><td>1 in [265]</td><td>1 <0.006</td>
<td>0.047 <</td><td>1 in [228]</td><td>| <</td><td>0.049</td><td>0.003 <</td><td>1 in [266]</td><td>1 <0.005</td>
<td>0.045 <</td><td>1 in [229]</td><td>1 <</td><td>0.047</td><td>0.003 <</td><td>1 in [267]</td><td>1 <0.005</td>
<td>0.043 <</td><td>1 in [230]</td><td>I <</td><td>0.045</td><td>0.003 <</td><td>1 in [268]</td><td>1 <0.005</td>
<td>0.040 <</td><td>1 in [231]</td><td>I <</td><td>0.042</td><td>0.003 <</td><td>1 in [269]</td><td>1 <0.005</td>
<td>0.038 <</td><td>1 in [232]</td><td>1 <</td><td>0.040</td><td>0.002 <</td><td>and [270]</td><td>1 <0.004</td>
<td>0.036 <</td><td>1 in [233]</td><td>I <</td><td>0.038</td><td>0.002 <</td><td>and [271]</td><td>1 <0.004</td>
<td>0.034 <</td><td>1 in [234]</td><td>1 <</td><td>0.036</td><td>0.002 <</td><td>and [272]</td><td>1 <0.004</td>
<td>0.032 <</td><td>1 in [235]</td><td>I <</td><td>0.034</td><td>0.001 <</td><td>and [273]</td><td>I <0.003</td>
<td>0.030 <</td><td>1 in [236]</td><td>| <</td><td>0.032</td><td>0.001 <</td><td>and [274)</td><td>1 <0.003</td>
<td>0.028 <</td><td>1 in [237]</td><td>| <</td><td>0.030</td><td>0.001 <</td><td>and [275]</td><td>1 <0.003</td>
<td>0.027 <</td><td>1 in [238]</td><td>I <</td><td>0.029</td><td>0.001 <</td><td>and [276]</td><td>1 <0.003</td>
<td>0.025 <</td><td>1 in [239]</td><td>| <</td><td>0.027.</td><td>0.000 <</td><td>and [277]</td><td>1 <0.002</td>
<td>0.023 <</td><td>1 in [240]</td><td>I <</td><td>0.025</td><td>0.000 <</td><td>and [278]</td><td>1 <0.002</td>
<td>0.022 <</td><td>1 in [241]</td><td>I <</td><td>0.024</td><td>0.000 <</td><td>and [279]</td><td>1 <0.002</td>
<td>0.021 <</td><td>1 in [242]</td><td>I <</td><td>0.023</td><td>0.000 <</td><td>and [280]</td><td>1 <0.002</td>
<td>0.019 <</td><td>1 in [243]</td><td>I <</td><td>0.021</td><td>0.000 <</td><td>and [281]</td><td>1 <0.002</td>
<td>0.018 <</td><td>1 in [244]</td><td>I <</td><td>0.020</td><td>0.000 <</td><td>and [282]</td><td>1 <0.002</td>
<td>0.017 <</td><td>1 in [245]</td><td>I <</td><td>0.019</td><td>-0.001 <</td><td>1 in [283]</td><td>1 <0.001</td>
<td>0.016 <</td><td>1 in [246]</td><td>I <</td><td>0.018</td><td>-0.001 <</td><td>1 in [284]</td><td>1 <0.001</td>
<td>0.015 <</td><td>1 in [247]</td><td>| <</td><td>0.017</td><td>-0.001 <</td><td>1 in [285]</td><td>1 <0.001</td>
<td>0.014 <</td><td>1 in [248]</td><td>| <</td><td>0.016</td><td>-0.001 <</td><td>1 in [286]</td><td>1 <0.001</td>
<td>0.013 <</td><td>1 in [249]</td><td>I <</td><td>0.015</td><td>0.000 <</td><td>and [287]</td><td>1 <0.002</td>
<td>0.012 <</td><td>1 in [250]</td><td>I <</td><td>0.014</td><td>, 0.000 <</td><td>and [288]</td><td>I <0.002</td>
<td>0.011 <</td><td>1 in [251]</td><td>| <</td><td>0.013</td><td>0.000 <|</td><td>and [289]</td><td>1 <0.002</td>
<td>0.010 <</td><td>And in [252]</td><td>I <</td><td>0012</td><td>0.000 <|</td><td>and [290]</td><td>1 <0.002</td>
<td>0.009 <</td><td>1 in [253]</td><td>I <</td><td>0011</td><td>0.000 <|</td><td>and [291]</td><td>1 <0.002</td>
<td>0.009 <</td><td>1 in [254]</td><td>I <</td><td>0011</td><td>0.001 <|</td><td>and [292]</td><td>1 <0.003</td>
<td>0.008 <</td><td>1 in [255]</td><td>I <</td><td>0.010</td><td>0.001 <|</td><td>and [293]</td><td>1 <0.003</td>
<td>0.007 <</td><td>And in [256]</td><td>I <</td><td>0.009</td><td>0.001 <|</td><td>and [294]</td><td>1 <0.003</td>
<td>0.007 <</td><td>And in [257]</td><td>I <</td><td>0.009</td><td>0.001 <|</td><td>and [295]</td><td>1 <0.003</td>
<td>0.006 <</td><td>1 in [258]</td><td>| <</td><td>0.008</td><td>0.000 <|</td><td>and [296]</td><td>1 <0.002</td>
<td>0.006 <</td><td>1 in [259]</td><td>I <</td><td>0.008</td><td>0.000 <1</td><td>and [297]</td><td>1 <0.002</td>
<td>0.006 <</td><td>1 in [260]</td><td>| <</td><td>0.008</td><td>0.000 <|</td><td>and [298]</td><td>1 <0.002</td>
<td>0.005 <</td><td>1 in [261]</td><td>| <</td><td>0.007</td><td>-0.001 <</td><td>and [299]</td><td>1 <0.001</td>
<td>0.005 <</td><td>1 in [262]</td><td>| <</td><td>0.007</td><td>-0.001 <</td><td>and [300]</td><td>1 <0.001</td>
<td>0.004 <</td><td>1 in [263]</td><td>I <</td><td>0.006</td><td>0.000 <|</td><td>and [301]</td><td>1 <0.002</td>
103
<td>0.000</td><td><1</td><td>w (302]</td><td>| <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in [340] |</td><td><</td><td>0.002</td>
<td>0.001</td><td><1</td><td>and [303]</td><td>I <</td><td>0.003</td><td>0.000</td><td><</td><td>1 in [341] |</td><td><</td><td>0.002</td>
<td>0.001</td><td><1</td><td>and [304]</td><td>I <</td><td>0.003</td><td>0.000</td><td><</td><td>1 in [342] |</td><td><</td><td>0.002</td>
<td>0.002</td><td><1</td><td>and [305]</td><td>| <</td><td>0.004</td><td>0.000</td><td><</td><td>1 in [343] |</td><td><</td><td>0.002</td>
<td>0.002</td><td><1</td><td>and [306]</td><td>1 <</td><td>0.004.</td><td>-0,001</td><td><</td><td>1 in [344] |</td><td><</td><td>0.001</td>
<td>0.002</td><td><|</td><td>and [307]</td><td>I <</td><td>0.004</td><td>-0,001</td><td><</td><td>1 in [345] |</td><td><</td><td>0.001</td>
<td>0.003</td><td><1</td><td>and [308]</td><td>| <</td><td>0.005</td><td>0.000</td><td><</td><td>1 in [346] |</td><td><</td><td>0.002</td>
<td>0.003</td><td><1</td><td>and [309]</td><td>I <</td><td>0.005</td><td>0.000</td><td><</td><td>1 in [347J |</td><td><</td><td>0.002</td>
<td>0.003</td><td><1</td><td>and [310]</td><td>I <</td><td>0.005</td><td>0.001</td><td><</td><td>1 in [348] 1</td><td><</td><td>0.003</td>
<td>0.004</td><td><1</td><td>and [311)</td><td>I <</td><td>0.006</td><td>0.001</td><td><</td><td>1 in [349] |</td><td><</td><td>0.003</td>
<td>0.004</td><td><1</td><td>and [312]</td><td>I <</td><td>0.006</td><td>0.001</td><td><</td><td>1 in [350] |</td><td><</td><td>0.003</td>
<td>0.004</td><td><1</td><td>and [313]</td><td>I <</td><td>0.006</td><td>0.002</td><td><</td><td>1 in [35l] |</td><td><</td><td>0.004</td>
<td>0.004</td><td><1</td><td>and [314]</td><td>| <</td><td>0.006</td><td>0.002</td><td><</td><td>1 in [352] |</td><td><</td><td>0.004</td>
<td>0.004</td><td><1</td><td>and [315]</td><td>I <</td><td>0.006</td><td>0.002</td><td><</td><td>1 in [353] |</td><td><</td><td>0.004</td>
<td>0.004</td><td><1</td><td>and [316]</td><td>| <</td><td>0.006</td><td>0.002</td><td><</td><td>1 in [354] |</td><td><</td><td>0.004</td>
<td>0.003</td><td><1</td><td>and [317]</td><td>I <</td><td>0.005</td><td>0.002</td><td><</td><td>1 in [355] |</td><td><</td><td>0.004</td>
<td>0.003</td><td><1</td><td>and [318]</td><td>1 <</td><td>0.005</td><td>0.001</td><td><</td><td>1 in [356] |</td><td><</td><td>0.003</td>
<td>0.003</td><td><|</td><td>and [319J</td><td>| <</td><td>0.005</td><td>0.001</td><td><</td><td>1 in [357] |</td><td><</td><td>0.003</td>
<td>0.003</td><td><1</td><td>and [320]</td><td>I <</td><td>0.005</td><td>0.001</td><td><</td><td>1 in [358] |</td><td><</td><td>0.003</td>
<td>0.002</td><td><1</td><td>and [321]</td><td>| <</td><td>0.004</td><td>0.001</td><td><</td><td>1 in [359] |</td><td><</td><td>0.003</td>
<td>0.002</td><td><1</td><td>and [322]</td><td>1 <</td><td>0.004</td><td>0.001</td><td><</td><td>1 in [360] |</td><td><</td><td>0.003</td>
<td>0.002</td><td><1</td><td>and [3231</td><td>I <</td><td>0.004</td><td>0.000</td><td><</td><td>1 in [361] |</td><td><</td><td>0.002</td>
<td>0.001</td><td><|</td><td>and [324]</td><td>| <</td><td>0.003</td><td>0.000</td><td><</td><td>1 in [362] |</td><td><</td><td>0.002</td>
<td>0.001</td><td><1</td><td>and [325]</td><td>I <</td><td>0.003</td><td>0.000</td><td><</td><td>1 in [363] |</td><td><</td><td>0.002</td>
<td>0.001</td><td><I</td><td>and [326]</td><td>| <</td><td>0.003</td><td>-0,001</td><td><</td><td>1 in [364] |</td><td><</td><td>0.001</td>
<td>0.000</td><td><1</td><td>and [327]</td><td>I <</td><td>0.002</td><td>-0,001</td><td><</td><td>1 in [365] |</td><td><</td><td>0.001</td>
<td>0.000</td><td><|</td><td>and [328]</td><td>I <</td><td>0.002</td><td>-0,001</td><td><</td><td>1 in [366] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [329]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [367] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [330]</td><td>| <</td><td>0.001</td><td>0.000</td><td><</td><td>1 in [368] |</td><td><</td><td>0.002</td>
<td>-0,001</td><td><1</td><td>and [331]</td><td>| <</td><td>0.001</td><td>0.000</td><td><</td><td>1 in [369] |</td><td><</td><td>0.002</td>
<td>-0,001</td><td><1</td><td>and [332]</td><td>| <</td><td>0.001</td><td>0.000</td><td><</td><td>1 in [370] |</td><td><</td><td>0.002</td>
<td>-0,001</td><td><|</td><td>and [333]</td><td>I <</td><td>0.001</td><td>0.000</td><td><</td><td>1 in [371] |</td><td><</td><td>0.002</td>
<td>0.000</td><td><1</td><td>and [334]</td><td>1 <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in [372] |</td><td><</td><td>0.002</td>
<td>0.000</td><td><1</td><td>and [335]</td><td>I <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in [373] |</td><td><</td><td>0.002</td>
<td>0.000</td><td><1</td><td>and [336]</td><td>and <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in [374] |</td><td><</td><td>0.002</td>
<td>0.000</td><td><1</td><td>and [337]</td><td>| <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in {375] |</td><td><</td><td>0.002</td>
<td>0.000</td><td><I</td><td>and [338]</td><td>| <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in [376] |</td><td><</td><td>0.002</td>
<td>0.000</td><td><1</td><td>and [339]</td><td>| <</td><td>0.002</td><td>0.000</td><td><</td><td>1 in [377] |</td><td><</td><td>0.002</td>
104
<td>0.000</td><td><</td><td>1 W [378] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [416] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [379] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 W [417] 1</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [380] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 W [418] 1</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [381] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [419] 1</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [382] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 W [42O] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [383] 1</td><td><0.002</td><td>-0,001</td><td><</td><td>1 W [421] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [384] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 W [422] |</td><td><0.001</td>
<td></td><td></td><td>. . .</td><td></td><td></td><td></td><td></td><td></td>
<td>u. uuu</td><td><</td><td>1 W [J03J 1</td><td><u.uuz</td><td>-0,001</td><td><</td><td>1 WL423]</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [386] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [424] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [387])</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [425] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [388] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [426] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [389] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [427] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [390] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [428] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [391] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [429] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [392] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [43O] |</td><td><0.001</td>
<td>0.000</td><td><</td><td>1 in [393] |</td><td><0.002</td><td>-0,001</td><td><</td><td>1 in [431] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [394] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [432] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in (395] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [433] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [396] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [434] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [397] |</td><td><0.001 '</td><td>-0,001</td><td><</td><td>1 in [435] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [398] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [436] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [399] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [437] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>And in [400] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [438] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [401] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [439] 1</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [402] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [440] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [403] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [441] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [404] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [442] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [405] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [443] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>| in [406] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [444] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [407] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [445] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>And in [408] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [446] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>And in [409]</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [447] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [410] Ί</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [448] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [411] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [449] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [412] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [450] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [413] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [451] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [414] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [452] |</td><td><0.001</td>
<td>-0,001</td><td><</td><td>1 in [415] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [453] |</td><td><0.001</td>
105
<td>-0,001</td><td><1</td><td>and [454]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [492] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>in [455)</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>and W [493] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [456]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [494] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [457]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [495] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>in [458]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [496] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [459]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [497]</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [460}</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [498] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [461]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [499] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [462]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [500] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [463]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [5O1] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [464]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [502] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [465]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [503] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>in [4 66]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [504] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>in [4 67]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [505] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [468]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [506] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [469]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>Iw [507] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [470]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [508] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [471]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [509] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [472]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [510] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [473]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [511] 1</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>in [474]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [512] 1</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [475]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [513] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [476]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [514] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><t</td><td>and [477]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [515] 1</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [478]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [516] |</td><td><</td><td>0.001</td>
<td>0.000</td><td><1</td><td>and [479]</td><td>1 <</td><td>0.002</td><td>-0,001</td><td><</td><td>1 in [517] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [480]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [518] 1</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [481]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [519]</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [482]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [520]</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [483]</td><td>1 <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [521] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [484]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [522] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [485]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [523] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [486]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [524] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [487]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [525] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>in [4 88]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [526] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><|</td><td>and [489]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [527] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [490]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [528] |</td><td><</td><td>0.001</td>
<td>-0,001</td><td><1</td><td>and [491]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [529] 1</td><td><</td><td>0.001</td>
106
<td>001</td><td><1</td><td>and [530]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [568] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [531]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [569]</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [532]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [570] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [533]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [571]</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [534]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [572] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [535]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [573] 1</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [536]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [574] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [537]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [575] And</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>w (538]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [576] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [539]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [577] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [540]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [578] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [541]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 W [579]</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [542]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [580] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [543]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [581] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [544]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [582] |</td><td><</td><td>O .001</td>
<td>001</td><td><|</td><td>and [545]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [583] 1</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [546]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [584] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [547]</td><td>1 <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [585] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [548]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [586] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [549]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [587] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [550]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [588] 1</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [551]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [589] 1</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [552]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [590] |</td><td><</td><td>0.001</td>
<td>001</td><td><Ί</td><td>and [553]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [591] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [554]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [592] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [555]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [593] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [556]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [594] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [557]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [595] 1</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [558]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [596] 1</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [559]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [597] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [560]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [598] 1</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [561]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [599] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [562]</td><td>| <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [600] |</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [563]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [601] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [564]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [602] 1</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [565]</td><td>| <</td><td>0.001</td><td>-Ó.001</td><td><</td><td>1 in [603] 1</td><td><</td><td>0.001</td>
<td>001</td><td><1</td><td>and [566]</td><td>I <</td><td>0.001</td><td>-0,001</td><td><</td><td>And in [604] |</td><td><</td><td>0.001</td>
<td>001</td><td><|</td><td>and [567)</td><td>1 <</td><td>0.001</td><td>-0,001</td><td><</td><td>1 in [605] |</td><td><</td><td>0.001</td>
107
<td>001</td><td><1</td><td>in [606] |</td><td><0.001</td><td>-0,001</td><td><</td><td>| and [623]</td><td>I <</td><td>0.001</td>
<td>001</td><td><|</td><td>in [607] |</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [624]</td><td>| <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [608] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [625]</td><td>I <</td><td>0.001</td>
<td>001</td><td><|</td><td>in [609] |</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [626]</td><td>I <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [610] |</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [627]</td><td>| <</td><td>0.001</td>
<td>001</td><td><|</td><td>in [611] |</td><td><0.001</td><td>· -0.001</td><td><</td><td>1 in [628]</td><td>1 <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [612] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [629]</td><td>| <</td><td>0.001</td>
<td>001</td><td><|</td><td>in [613] 1</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [630]</td><td>I <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [614] |</td><td><0.001</td><td>-0,001</td><td><</td><td>| and [631]</td><td>| <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [615] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [632]</td><td>I <</td><td>0.001</td>
<td>001</td><td><|</td><td>in [616] |</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [633]</td><td>I <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [617] |</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [634]</td><td>| <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [618] |</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [635]</td><td>1 <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [619] 1</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [636]</td><td>| <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [620]</td><td><0.001</td><td>-0,001</td><td><</td><td>1 in [637]</td><td>I <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [621] |</td><td><0.001</td><td>-0,001</td><td><</td><td>| and [638]</td><td>| <</td><td>0.001</td>
<td>001</td><td><1</td><td>in [622] |</td><td><0.001</td><td>-0,001</td><td><</td><td>And in [639]</td><td>| <</td><td>0.001</td>
Fraunhofer Gesellschaft zur Forderung der angewandten Forschung e. V., Germany Plenipotentiary:
108
EP 2 076 901 B1
Z-15889/17
Contents3
138 members in 26 offices
Priority claims5
| Document | Office | Kind | Date |
|---|---|---|---|
| 86295406 | United States of America | P | |
| 86295406 | United States of America | P | |
| 078192598 | – | – | – |
| 862954P | – | – | – |
| US20060862954P | – | – | – |
Members138
| Document | Office | Kind | |
|---|---|---|---|
| AU2007308415A1 | Australia | A1 | |
| AU2007308416A1 | Australia | A1 | |
| CA2645618A1 | Canada | A1 | |
| CA2667505A1 | Canada | A1 | |
| WO2008049589A1 | World Intellectual Property Organization (WIPO) | A1 | |
| WO2008049590A1 | World Intellectual Property Organization (WIPO) | A1 | |
| TW200836166A | Taiwan Province of China | A | |
| TW200837719A | Taiwan Province of China | A | |
| MX2008011898A | Mexico | A | |
| KR20080102222A | Republic of Korea | A | |
| EP1994530A1 | European Patent Office (EPO) | A1 | |
| AR063394A1 | Argentina | A1 | |
| AR063400A1 | Argentina | A1 | |
| HK1119824A | Hong Kong, China | A | |
| HK1119824A1 | Hong Kong, China | A1 | |
| CN101405791A | China | A | |
| MX2009004477A | Mexico | A | |
| KR20090058029A | Republic of Korea | A | |
| EP1994530B1 | European Patent Office (EPO) | B1 | |
| EP2076901A1 | European Patent Office (EPO) | A1 | |
| AT435480T | Austria | T | |
| ATE435480T1 | Austria | T1 | |
| NO20084012L | Norway | L | |
| NO20091951L | Norway | L | |
| NO20170452A1 | Norway | A1 | |
| DE602007001460D1 | Germany | D1 | |
| JP2009530675A | Japan | A | |
| DK1994530T3 | Denmark | T3 | |
| PT1994530E | Portugal | E | |
| EP2109098A2 | European Patent Office (EPO) | A2 | |
| ES2328187T3 | Spain | T3 | |
| CN101606194A | China | A | |
| IL197976A0 | Israel | A0 | |
| IL197976D0 | Israel | D0 | |
| US2009319283A1 | United States of America | A1 | |
| ZA200810308B | South Africa | B | |
| PL1994530T3 | Poland | T3 | |
| US2010023322A1 | United States of America | A1 | |
| JP2010507820A | Japan | A | |
| RU2008137468A | Russian Federation | A | |
| ZA200902199B | South Africa | B | |
| KR100957711B1 | Republic of Korea | B1 | |
| AU2007308416B2 | Australia | B2 | |
| AU2007308415B2 | Australia | B2 | |
| RU2009119456A | Russian Federation | A | |
| MY142520A | Malaysia | A | |
| RU2411645C2 | Russian Federation | C2 | |
| RU2420815C2 | Russian Federation | C2 | |
| BRPI0709310A2 | Brazil | A2 | |
| KR101056253B1 | Republic of Korea | B1 | |
| IL193786A | Israel | A | |
| TWI355649B | Taiwan Province of China | B | |
| CN101405791B | China | B | |
| TWI357065B | Taiwan Province of China | B | |
| JP4936569B2 | Japan | B2 | |
| CN101606194B | China | B | |
| JP5083779B2 | Japan | B2 | |
| CA2645618C | Canada | C | |
| US8438015B2 | United States of America | B2 | |
| US8452605B2 | United States of America | B2 | |
| MY148715A | Malaysia | A | |
| US2013238343A1 | United States of America | A1 | |
| IL197976A | Israel | A | |
| US8775193B2 | United States of America | B2 | |
| CA2667505C | Canada | C | |
| EP2076901B1 | European Patent Office (EPO) | B1 | |
| BRPI0716315A2 | Brazil | A2 | |
| EP2109098A3 | European Patent Office (EPO) | A3 | |
| EP2076901B8 | European Patent Office (EPO) | B8 | |
| PT2076901T | Portugal | T | |
| ES2631906T3 | Spain | T3 | |
| PL2076901T3This record | Poland | T3 | |
| NO341567B1 | Norway | B1 | |
| NO341610B1 | Norway | B1 | |
| EP3288027A1 | European Patent Office (EPO) | A1 | |
| NO342691B1 | Norway | B1 | |
| HK1251073A | Hong Kong, China | A | |
| HK1251073A1 | Hong Kong, China | A1 | |
| BRPI0709310B1 | Brazil | B1 | |
| EP2109098B1 | European Patent Office (EPO) | B1 | |
| PT2109098T | Portugal | T | |
| PL2109098T3 | Poland | T3 | |
| EP3288027B1 | European Patent Office (EPO) | B1 | |
| ES2834024T3 | Spain | T3 | |
| PT3288027T | Portugal | T | |
| EP3848928A1 | European Patent Office (EPO) | A1 | |
| PL3288027T3 | Poland | T3 | |
| ES2873254T3 | Spain | T3 | |
| EP3848928B1 | European Patent Office (EPO) | B1 | |
| FI3848928T3 | Finland | T3 | |
| PT3848928T | Portugal | T | |
| DK3848928T3 | Denmark | T3 | |
| EP4207189A1 | European Patent Office (EPO) | A1 | |
| PL3848928T3 | Poland | T3 | |
| ES2947516T3 | Spain | T3 | |
| EP4207189B1 | European Patent Office (EPO) | B1 | |
| EP4207189C0 | European Patent Office (EPO) | C0 | |
| EP4300824A2 | European Patent Office (EPO) | A2 | |
| EP4300825A2 | European Patent Office (EPO) | A2 | |
| EP4325723A2 | European Patent Office (EPO) | A2 |
Numbers
- Publication
- 2076901
- Publication, DOCDB
- 2076901
- Publication, EPODOC
- PL2076901T
- Application
- 7819259
- Application, DOCDB
- 07819259
- Application, EPODOC
- PL20070819259T
Titles2
- English
- APPARATUS AND METHOD FOR GENERATING AUDIO SUBBAND VALUES AND APPARATUS AND METHOD FOR GENERATING TIME-DOMAIN AUDIO SAMPLES
- Polish
- Urządzenie i sposób do generowania wartości podpasm audio i urządzenie i sposób do generowania próbek audio w dziedzinie czasu
Classification
- CPC, 8
- G10L19/022
- G10L19/0204
- G10L19/02
- H03H17/0266
- G10L21/038
- G10L25/45
- G11B20/10
- H03M7/30
- IPC, 2
- G10L19 022
- G10L19 02