Apparatus and method for generating audio subband values and apparatus and method for generating time-domain audio samples

Technical Field [0001] Variants of the present invention relate to a device and method for generating audio subrange values, a device and method for generating audio signal samples in the time domain, and systems including any of the above devices that can be used in the field of modern audio signal coding, audio signal decoding and other applications related to the transmission of audio signals.

[0002] Modern digital audio signal processing is usually based on coding schemes that significantly reduce the bit rate, bandwidth required during transmission, and memory space compared to direct transmission or storage of audio data. This was achieved by encoding the audio data on the sender side and decoding the encoded data on the receiver side before, for example, presenting the decoded audio data to the listener or subjecting it to further processing.

[0003] Such systems for processing digital audio signals can be implemented with respect to a wide range of parameters, which usually has an impact on the one hand on the quality of the audio signal transmitted or otherwise processed, and on the other hand on computational efficiency, bandwidths and other performance related parameters. Higher quality is often associated with higher bit rates, increased computational complexity, and greater memory requirements in which encoded audio data is stored. Depending on the particular application, in order to achieve the desired and achievable quality, a balance should be ensured between factors such as permissible bit rates, permissible computational complexity and permissible data volume.

[0004] Another parameter that can play a significant role, especially for real-time applications such as bidirectional or unidirectional communication, is the delay introduced by various coding schemes. As a result, the delay introduced by audio coding and decoding is a limitation associated with the above parameters that should be considered when balancing the requirements and costs of the various coding schemes used in specific applications. Because systems based on digital audio signals can be used in many different areas, ranging from very low quality transmission to very high-end transmission, such audio systems often have differing parameters and restrictions. For some applications, a lower delay may, for example, require a higher bit rate and therefore also a larger bandwidth compared to audio systems where the delay is higher (while maintaining comparable quality).

[0005] In many cases, however, there may be a need to compromise between different parameters such as bit rate, computational complexity, memory requirement, quality and delay.

[0006] Document US 6,748,363 B1 relates to a TI window compression / expansion method. This publication describes a proprietary technique for compressing arrays of audio signal encoder windows to a size equal to 1/8 or less of the original size without any loss of quality. The technique of reducing the requirements for memory space occupied by the tables of windows of audio coders is based on multiple differentiation. Because the difference between any two adjacent samples in the first differential signal is small, it is more efficient to store this difference. This technique can be used several times as long as the results obtained are smaller in size, while the computational complexity of the decompression process increases. The optimal number of repetitions depends on the specific application and shape of the window.

[0007] Document US 2005/102150 A1 relates to a method of filtering the analysis / synthesis of a band subband. This publication describes a method of encoding / decoding audio signals that enables the encoding of an audio source signal and the decoding of multiple subband samples to generate a digital audio source signal. During the coding process, this method performs a summation of P windowed audio samples according to 2P time domain intervals, the sum from the first to (M-1) sum according to 2P windowed audio samples according to 2P time domain intervals, and the calculation of M subband samples according to M sums. During the decoding process, the M subband samples are read in accordance with the plurality of subband samples corresponding to the first variable value indicator, so that it is possible to generate a digital audio source signal using inverse discrete cosine transform and synthesis operations.

[0008] US 6,707,869 B1 relates to a signal processing device equipped with a filter with variable window structure. This publication describes a filter enabling the processing of a digital signal using a window function. The filter has a memory that allows storing a basic set of values ​​representing a single window. The adapter allows to generate based on this basic set of many adapted sets of values, with the adapted sets of values ​​specifying various window functions with differing window sizes. The adapter has an input intended for receiving a control signal, which enables the selection of a suitable adapted set to match the processed digital signal. The window function is used to process subsequent digital signal frames using the adapted set of values ​​generated by the adapter in response to the received control signal.

[0009] Document EP 1 160 977 A relates to a method and apparatus for reducing aliasing in cascade filter banks. This publication describes a method and apparatus for reducing aliasing between adjacent sub-ranges in cascade filter banks. The aliasing-reducing filter bank is used to reduce the aliasing components between different sub-ranges of the band. The response module and phase of the aliasing-reducing filter bank is usually similar to the synthesis filter bank response module in the first-stage filter bank. The aliasing-reducing filter bank allows filtering and summing of signals from the set of M2 subranges of the band from the M1 subranges of the first-order analysis filter bank band. After performing the aliasing reduction step using the next analysis filter bank, a higher frequency resolution is obtained. The signals contained in these subbands are first introduced to the bank of filters reducing aliasing in order to reduce aliasing. If the first stage filter bank is in the form of a modulated fixed filter bank with M1 bands, and the aliasing reduction stage includes M2 bands, in order to achieve aliasing reduction, the aliasing reduction filter bank must have a similar frequency response as the synthesis filter bank used in the first stage, but the frequency musi must be scaled using the sample rate, M1 / ​​M2. After the stage of using the bank of filters that reduce aliasing, processing using the analysis filter bank is used to obtain a higher frequency frequency resolution. The synthesis filter bank corresponding to the first stage analysis filter bank can be reduced by storing only each M1 / ​​M2 substructure in order to obtain an aliasing filter bank.

[0010] US 5,809,474 A relates to an audio encoder using a fast analysis filter algorithm and an audio decoder using a fast synthesis filter algorithm. This publication describes an audio encoder / decoder using a fast analysis filter algorithm. The audio encoder includes a mapping module enabling the classification of the received audio signal according to the frequency range using a fast range filtering algorithm, a psychoacoustic model of assigning bits to each frequency range using psychoacoustic characteristics, a quantizing and coding module enabling the quantization and coding of the mapped signal according to the number of bits allocated to each of the frequency ranges, and a frame compressing module enabling the generation of a bit stream based on the output signal of the quantizing and coding module. The audio decoder includes a decompression module that allows decompression of the signal from the encoded and received bit stream, a module decoding and performing an inverse process for quantization enabling decoding and performing an inverse process for quantizing a quantized signal, and a module performing an inverse mapping process enabling performing inverse mapping of a signal subjected to an inverse quantization process using a fast range synthesis filtering algorithm.

Summary [0011] In one embodiment of the present invention, the device for generating the audio subband values ​​in the audio subband channels includes an analysis window module that allows windowing of the input frame of audio samples in the time domain in a time sequence from the previous sample to the later sample using the window analysis function including the sequence of window coefficients to obtain windowed samples, wherein the window function of analysis includes a first number of window coefficients obtained based on a larger window function comprising the sequence of a larger second number of window coefficients, where the window function coefficients of the window function are obtained by interpolation of the coefficients of a larger window function and the second number is an even number, and a calculator enabling calculation band subrange values ​​using windowed samples.

[0012] In one embodiment of the present invention, the device for generating time-domain audio signal samples includes a calculator that allows calculating intermediate sequence of time-domain samples based on audio subband values ​​in the audio subband channels, the sequence including prior intermediate time-domain audio signal samples and subsequent intermediate time-domain audio signal samples; a synthesis window module that allows windowing of intermediate time sequence samples using a synthesis window function involving a window coefficient sequence to obtain windowed time domain samples, where the synthesis window function includes the first number of window coefficients obtained based on a larger window function including a larger second sequence number of window coefficients, window coefficients of the window function are obtained by interpolation of the coefficients of the larger window function and the second number is an even number, and the initial step performing the overlap with the addition that allows processing of windowed intermediate time domain samples to obtain time domain samples.

Brief Description of the Drawings [0013] Variants of the present invention are set out below with reference to the accompanying drawings.

Fig. 1 shows a block diagram of one embodiment of an apparatus for generating audio subband values;

Fig. 2a is a block diagram of one embodiment of an apparatus for generating time domain audio samples;

Fig. 2b illustrates the operating principle of one embodiment of the present invention in the form of a device for generating time-domain samples;

Fig. 3 illustrates the concept of interpolation of window coefficients used in one 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 one embodiment of the present invention comprising an SBR decoder and an SBR encoder;

Fig. 6 shows the sources of delays in the SBR system;

Fig. 7a is a flowchart of one embodiment of a method of generating an audio subband value;

Fig. 7b shows one of the steps of the method shown in fig. 7a;

Fig. 7c is a flowchart of one embodiment of a method of generating an audio subband value;

Fig. 8a is a flowchart of a comparative example of a method for generating time-domain samples;

Fig. 8b is a flowchart of a comparative example of a method for generating time-domain samples;

Fig. 8c is a flowchart of one embodiment of a method for generating time-domain samples;

Fig. 8d is a flowchart of another embodiment of a method for generating time-domain samples;

Fig. 9a shows a possible implementation of a comparative example of the method of generating audio subband values;

Fig. 9b illustrates a possible implementation of one embodiment of the method for generating audio subband values;

Fig. 10a illustrates a possible implementation of a comparative example of a method for generating time-domain samples;

Fig. 10b illustrates a possible implementation of one embodiment of the method for generating time-domain samples;

Fig. 11 shows a comparison of a synthesis window function according to one embodiment of the present invention and a sine window function;

Fig. 12 shows a comparison of the synthesis window function according to one embodiment of the present invention and the SBR QMF prototype filter function;

Fig. 13 shows the various delays introduced by the window function and the prototype filter function shown in Fig. 12;

Fig. 14a is a table illustrating various delay components of the conventional AAC-LD + SBR codec and the AAC-ELD codec comprising one embodiment of the present invention;

Fig. 14b shows another table containing details of the delays of the various elements of the various codecs;

Fig. 15a shows a comparison of frequency responses of devices based on a window function according to one embodiment of the present invention and a device based on a sine window function;

Fig. 15b is a close-up of the frequency response of Fig. 15a;

Fig. 16a shows a comparison of the frequency responses of 4 different window functions;

Fig. 16b is a close-up of the frequency responses of Fig. 16a;

Fig. 17 shows a comparison of the frequency responses of two different window functions - the window function according to the present invention and the window function being a symmetrical window function;

Fig. 18 schematically shows the general time masking properties of the human ear; and

Fig. 19 shows a comparison of an original audio time signal, a time signal generated using a HEAAC codec, and a codec-based time signal comprising one embodiment of the present invention.

Detailed Description of Embodiments of the Invention [0014] Figs. 1 to 19 show block diagrams and other diagrams describing the functional properties and features of various embodiments of methods and devices for generating audio subband values, methods and devices for generating time and systems samples including at least one of said methods and devices. 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 or in software. The implementations described in the form of block diagrams of hardware implementations of the respective embodiments of the invention can therefore also be considered as the operation diagrams of the respective embodiments of the method of the invention. A flowchart of an embodiment of the present invention can also be considered as a block diagram of the corresponding hardware implementation.

[0015] The implementations of filter banks that can be used as an analysis filter bank or a synthesis filter bank are described below. The analysis filter bank is a device for generating audio subband values ​​in the audio subband channels based on (input) time domain audio samples in the form of a time sequence extending from the previous sample to the later sample. In other words, the term analysis filter bank can be used synonymously to implement the present invention in the form of a device for generating audio subband values. The synthesis filter bank is therefore a device for generating time-domain audio signal samples based on audio subband values ​​in the audio subband channels. In other words, the term synthesis filter bank can be used synonymously to implement the present invention in the form of a device for generating time-domain audio signal samples.

[0016] The analysis filter bank and the synthesis filter bank, also generally called filter banks, can for example be implemented in the form of modulated filter banks. Modulated filter banks, examples and embodiments of which will be presented in more detail later in the description, are based on vibrations with frequencies obtained on the basis of the central frequencies of the corresponding subranges in the frequency domain. The term "modulated" refers in this context to the fact that the above-mentioned vibrations are used together with a window function or a prototype filter function, depending on the specific implementation of the modulated filter bank. Modulated filter banks can in principle be based on real-value vibrations, such as harmonic vibrations (sinusoidal vibrations or cosine waves) or complex vibrations (exponential disappearing vibrations). Modulated filter banks are therefore called respectively modulated real filter banks or modulated complex filter banks.

[0017] The following describes in more detail the embodiments of the present invention in the form of modulated low-delay complex filter banks and modulated low-delay real filter banks, and corresponding software methods and implementations. One of the main applications of such modulated low-delay filter banks is their integration in low-latency replication spectrum reconstruction (SBR) systems, which are currently based on the use of the QMF complex filter bank with symmetrical prototype filter (QMF = mirror quadrature filter).

[0018] As will become apparent through the present description, the implementation of low-delay filter banks according to embodiments of the present invention provides the advantage of a better compromise between computational complexity, frequency response, noise distribution over time, and quality (reconstruction). It is also possible to achieve a better compromise between delay and reconstruction quality based on an approach using so-called zero delay techniques that aim to increase the impulse response of a filter belonging to the respective filter banks without introducing an additional delay. The use of an analysis filter bank or a synthesis filter bank according to embodiments of the present invention allows for less delay at a certain level of quality, better quality at a certain level of delay, or simultaneous improvement of delay and quality.

[0019] Embodiments of the present invention are based on the finding that said improvements can be obtained by using an interpolation scheme to obtain a window function having a first number of window coefficients based on a window function having a larger second number of window coefficients. By using the interpolation scheme it is possible to obtain a better distribution of the energy values ​​of the window coefficients of the window functions. In many cases, this leads to better aliasing and higher sound quality. An interpolation scheme may be useful, for example, if the larger window function includes an even number of window coefficients.

[0020] The use of the interpolation scheme only leads to a slight increase in computational complexity. This small increase, however, is not only associated with an increase in quality, but also a saving of memory used compared to a solution in which two separate window functions are stored independently of each other. Although interpolation can be performed in one or several cycles of the processor clock signal in a given implementation, which in many cases is associated with a slight delay and increase in computational complexity, in many applications additional memory requirements are extremely important. For example, for mobile applications, the amount of memory may be limited, especially if long window functions with a significant number of window coefficients are used.

[0021] Embodiments of the present invention can also be used in the context of a new window function to any of the two filter banks described above, which allows for even better compromises between the above-mentioned parameters. The quality and / or delay can be further improved for the analysis filter bank by using the analysis window function comprising a window coefficient sequence that includes the first group comprising the first part of the window coefficient sequence and the second window coefficient group comprising the second part of the window coefficient sequence. The first and second parts include all window coefficients for the window function. The first part further includes a smaller number of window coefficients than the second part, but the energy value of the window coefficients in the first part is greater than the energy value of the window coefficients in the second part. The first part of the window coefficients is used to window later samples in the time domain, while the second part of the window coefficients is used to window earlier samples in the time domain. This form of window function provides the possibility of earlier processing of time-domain samples using higher energy window coefficients. This is the result of the described distribution of window coefficients in two parts and their use to process sample sequences in the time domain. Consequently, the use of such a window function makes it possible to limit the delay introduced by the filter bank at a constant level of quality or to obtain a higher level of quality at a constant level of delays.

[0022] In the embodiment of the present invention in the form of a device for generating time-domain audio signal samples and a corresponding method, a window synthesis window function may be used in the window module comprising a sequence of window coefficients arranged in the first (sequentially) part and in the second (respectively) sequentially) parts. Also for the synthesis window function, the energy value and the total energy value of the window coefficients in the first part are greater than the energy value and the total energy value of the window coefficients in the second part, the first part comprising a smaller number of window coefficients than the second part. Due to such distribution of window coefficients in two parts and the use in the window module of the first part of the window coefficients when windowing later samples in the time domain and the second part of the window coefficients when windowing earlier samples in the time domain, the effects and advantages described above also apply to the synthesis filter bank and a corresponding embodiment of the method according to the invention.

[0023] More detailed descriptions of the synthesis window function and the analysis window function used in some embodiments of the present invention will be set forth below. In many embodiments of the present invention, the sequence of window coefficients of the synthesis window function and / or the analysis window function includes exactly the first group and the second group of window coefficients. Each of the window coefficients of the window coefficient sequence also belongs to the first or second group of window coefficients.

[0024] Each of the two groups comprises exactly one part of the sequence of successively arranged window coefficients. In this specification, the part includes another set of window coefficients arranged in accordance with the sequence of window coefficients. In some embodiments of the present invention, both groups (first and second groups) comprise exactly one part of the window coefficients arranged as described above. The corresponding groups of window coefficients do not contain window coefficients that do not belong exactly to one part of the corresponding group. In other words, in many embodiments of the present invention, both the first and second groups of window coefficients include only the first and second parts of the window coefficients, without any other window coefficients.

[0025] In the present description, the next part of the window coefficient sequence should be understood as a corresponding set of window coefficients in the mathematical sense, where compared to the sequence of window coefficients in the set there are no window coefficients that could be in the range (e.g. index range) of the coefficients windows of the relevant part. Consequently, in many embodiments of the present invention, the sequence of window coefficients is divided exactly into two interconnected parts of window coefficients, which constitute the first and second parts of the window coefficients. In such cases, each window coefficient in the first group of window coefficients is in front of or behind each of the window coefficients belonging to the second group of window coefficients with respect to the overall sequence of window coefficients.

[0026] In other words, in many embodiments of the present invention, the window coefficient sequence is divided into exactly two groups or parts, without leaving any window coefficients. According to the sequence of window coefficients, which also means their order, each of the two groups or parts includes all window coefficients up to (but not including) or from (including) the limit window coefficient. For example, the first part or first group may include window coefficients having indexes from 0 to 95 and 96 to 639 for a window function comprising 640 window coefficients (having indexes from 0 to 639). The index of the window will have the index 96 here. Of course, other examples are also possible (for example from 0 to 543 and from 544 to 639).

[0027] The exemplary implementation of the analysis filter bank described below provides a filter length of 10 blocks of input samples, with a system delay of only 2 blocks, which corresponds to the delay introduced by modified discrete cosine transform (MDCT) or modified discrete sine transform (MDST). One difference is the increase in the filter length of 10 blocks of input samples compared to 1 block when using modified discrete cosine transform (MDCT) or 9 blocks when using modified discrete sine transform (MDST). However, it is also possible to use implementations involving a different number of blocks of input samples, which are also called audio input samples.

[0028] It is also possible to develop and implement other trade-offs.

[0029] Fig. 1 is a block diagram of an analysis filter bank 100 constituting an embodiment of the device for generating audio subband values ​​in the audio subband channels. The analysis filter bank 100 includes an analysis window 110 allowing windowed frame 120 time input audio samples. Frame 120 includes T blocks 130-1, 130-T samples of the (input) audio signal in the time domain, where T is a positive integer which is equal to 10 in the embodiment of Figure 1. Frame 120 may, however, also include another number of blocks 130.

[0030] Both frame 12 and each of the blocks 130 include time-domain audio input samples in a time sequence from the previous sample to the later sample, according to the time line indicated by arrow 140 in Fig. 1. In other words, for fig . 1 the closer to the right is the time domain audio sample, which in this case is also the time domain audio input sample, the corresponding the time domain audio sample is later, given the time domain audio sample sequence.

[0031] The analysis window 110, based on the sequence of time-domain audio samples, generates windowed time-domain samples that are arranged in a frame of 150 windowed samples. According to a frame of 120 time domain audio input samples, also a frame of 150 windowed samples includes T blocks of windowed samples 160-1,., 160-T. In preferred embodiments of the present invention, each of the windowed sample blocks 160 includes a number of windowed samples equal to the number of time-domain audio input samples included in each of the blocks of 130 time-domain audio input samples. If each of the blocks 130 includes N input time domain audio samples, frame 120 and frame 150 thus include TN samples. In this case, N is a positive integer that can take, for example, 32 or 64. In the above case, for T-1 frames 120, 150 include 320 and 640, respectively.

[0032] The analysis window 110 is connected to a calculator 170 enabling the calculation of audio subband values ​​based on windowed samples provided by the analysis window module 110. The audio subband values ​​are provided by the calculator 170 in the form of a block 180 of audio subband values, each of the audio subband values ​​corresponds to one audio subband channel. In a preferred embodiment of the invention, also block 180 of the audio subband values ​​includes the N subband values.

[0033] Each of the subband channels of the audio signal corresponds to a specific center frequency. The center frequencies of different channels of the audio subband can be, for example, evenly spaced or equidistant from each other relative to the bandwidth of the corresponding audio signal band described by the time domain audio input samples provided by the analysis filter bank 100.

[0034] The analysis window 110 is adapted to window the input of the audio signal in the time domain of the frame 120 based on the analysis window function comprising a window coefficient sequence comprising the first number of window coefficients to obtain windowed frame 150 samples. The analysis window module 110 is adapted to perform the window process of the time domain audio sample frame 120 by multiplying the time domain audio sample values ​​and window coefficients of the window analysis function. In other words, windowing involves the component-dependent multiplication of time-domain audio samples by their corresponding window coefficients. Since the frame 120 of the time domain audio signal samples and window coefficients include the corresponding sequence, the element-dependent multiplication of the time domain audio signal samples and window coefficients is carried out according to their corresponding sequences, e.g. according to the samples and the window coefficient index.

[0035] In some embodiments of the present invention, the window functions used for windowing the time domain audio input sample frames are generated based on a larger window function including a larger second number of window coefficients using an interpolation scheme, for example such as described with reference to fig. . 3 and Fig. 4. The larger window function usually includes an even number of window coefficients and may, for example, be asymmetrical with respect to the sequence of window coefficients. It is also possible to use symmetrical window functions.

[0036] The window function 190 used to window the frame 120 of time-domain input samples can be obtained, for example, using an analysis window module 110 or a filter bank 100 interpolating the window coefficients of the larger window function. In some embodiments of the present invention, this is done, for example, by interpolating successive window coefficients of a larger window function. It is possible to use linear, polynomial or curve-based interpolation schemes.

[0037] For example, if each window coefficient of a larger window function is used once to generate a window coefficient of the window function and the second number is even, the number of window coefficients of the window function 190 (first number) is half of the second number. Such interpolation can be based on linear interpolation, an example of which will be given later in relation to equation (15). This is how it is described in this description, but it is also possible to use other interpolation schemes.

[0038] In the embodiments of the present invention in the form of an analysis filter bank 100, as shown in Figure 1, the analysis window function as well as the synthesis window function in the case of the synthesis filter bank may include, for example, only windowed coefficients with real values. In other words, each of the window coefficients assigned to the window coefficient index has a real value.

[0039] The window coefficients together form the corresponding window function in the form of the window function of analysis 190, an example of which is shown in Figure 1. The window functions that reduce the delay when used in the context of the filter banks described are discussed below. Embodiments of the present invention are, however, not limited to such low delay window functions.

[0040] The sequence of window coefficients forming the analysis window 190 includes the first group 200 and the second group 210 of window coefficients. The first group 200 includes the first part of the successive and successive window coefficients, while the second group 210 includes the second part of the successive and successive window coefficients. Together with the first part in the first group 200, they form the entire sequence of window coefficients of the 190 window analysis function. Each window coefficient belonging to the sequence of window coefficients furthermore belongs to the first part or to the second part of the window coefficients, so that the entire window function of the analysis 190 is formed by the window coefficients of the first part and the second part. The first part of the window coefficients is therefore identical to the first group of window coefficients 200, and the second part is identical to the second group of window coefficients 210, as indicated in Fig. 1 the corresponding arrows 200, 210.

[0041] The number of window coefficients in the first group 200 of the first part of the window coefficients is smaller than the number of window coefficients in the second group of the second part of the window coefficients. However, the energy value and the total energy value of the window coefficients in the first group 200 are greater than the energy value and the total energy value of the window coefficients in the second group 210. As will be presented later in this description, the energy value of the set of window coefficients is based on the sum of squares of the absolute values ​​of the respective window coefficients.

[0042] In some embodiments of the present invention, the window function of analysis 190 as well as the corresponding window function of synthesis may thus be asymmetrical with respect to the window coefficient sequence or window coefficient index. Based on the defining set of window coefficients for the window 190 function, the window 190 analysis function is asymmetrical if no real number exists for all real numbers n, so that the absolute value of the window coefficient corresponding to the window coefficient index (no-n) is not equal to the absolute value of the corresponding window factor (no + n) when (n0-n) and (no + n) belong to the defining set.

[0043] As shown schematically in Figure 1, the analysis window 190 also includes sign changes at which the product of two consecutive window coefficients is negative. Details and further properties of possible window functions according to embodiments of the present invention will be discussed with reference to Figures 11 to 19.

[0044] As noted earlier, the windowed sample frame 150 has a block structure comprising single blocks 160-1, 160-T and similar to a frame 120 consisting of single time domain input samples. Since the analysis window 110 is adapted to window the time domain audio input samples by multiplying these values ​​by the window coefficients of the analysis window function 190, the frame 150 of windowed samples is also determined in the time domain. The calculator 170 calculates the audio subrange values, and more precisely the block 180 of the audio sub range values, using a frame of 150 windowed samples, and then performs the transformation from the time domain to the frequency domain. The calculator 170 can thus be regarded as a time / frequency converter that allows providing a block 180 of the subrange values ​​of the audio signal constituting the spectral representation of the frame 150 of windowed samples.

[0045] Each sub-range value of the audio signal at block 180 corresponds to one sub-range with a specific frequency. The number of sub-range values ​​of the audio signal in block 180 is also sometimes called the number of bands.

[0046] In many embodiments of the present invention, the number of audio sub-range values ​​in block 180 is the same as the number of time domain audio input samples in each of the blocks 130 of frame 120. Where the frame 150 windowed samples has the same block structure as the frame 120, so that each block 160 windowed samples also includes the same number of windowed samples as the number of audio input samples in the time domain 130, block 180 values ​​of audio subranges naturally the same number as block 160.

[0047] Optionally, it is possible to generate frame 120 based on a block of new audio input samples in the time domain 220 by shifting blocks 130-1,., 130- (T-1) one block in the opposite direction to the arrow 140 indicating the direction of passage time. The frame 120 for processing time-domain audio input samples is generated by shifting (T-1) the last blocks of the immediately preceding time-domain audio signal frame 120 one block towards the earlier time-domain audio samples and adding a new block 220 new time domain audio signal samples as a new block 130-1 including the latest time domain audio signal samples of the current frame 120. In Fig. 1 this was also indicated by a series of dashed arrows

230 indicating block displacement, displacement of blocks 130-1, 130- (T-1) in the opposite direction to arrow 140.

[0048] Due to the offset of the blocks 130 in the opposite direction to the arrow 140 indicating the direction of elapsed time, the current frame 120 to be processed includes the block 130- (T-1) directly of the previous frame 120 as the new block 130T. Blocks 130- (T-1), 130-2 for processing the current frame 120 correspond to blocks 130- (T21),., 130-1 of the immediately previous frame 120. Block 130-T of the immediately previous frame 120 is skipped.

[0049] As a result, each time-domain audio signal sample of the new block 220 is processed T times during T subsequent processing processes T of successive frames 120 input time-domain audio signal samples. Therefore, each audio input signal sample in the time domain of the new block 220 is associated not only with T different frames 120, but also T different frames 150 windowed samples and T blocks 180 values ​​of the audio sub-ranges. As noted above, in a preferred embodiment of the present invention, the number of T blocks in frame 120 is 10, so that each time-domain audio signal sample entered in the analysis filter bank 100 corresponds to 10 different blocks 180 sub-ranges of the audio signal.

[0050] Initially, before a single frame 120 is processed by the analysis filter bank 100, the frame 120 may be initialized to a small absolute value (less than the specified threshold value), for example a value of 0. As will be described in more detail later in the description, the shape of the window function of analysis 190 includes a midpoint or "center of gravity" that typically corresponds or is located between two indexes of the window coefficients of the first group 200.

As a result, the number of new blocks 220 to be placed in the frame 120 is small before filling the frame 120 at least to the extent that the parts of the frame 120 occupied by non-disappearing (i.e. non-zero values) values ​​corresponding to window coefficients with a significant contribution from the point of view their energy values. The number of blocks to be placed in frame 120 before the "significant" processing can be started is usually between 2 and 4 blocks, depending on the shape of the 190 analysis window function. The analysis bank filter 100 therefore allows 180 blocks to be delivered faster than the corresponding filter bank using example of a symmetrical window function. Because new blocks 220 are usually introduced into the analysis bank filter 100 simultaneously, each of the new blocks corresponds to the recording or sampling time, which is essentially determined by the length of block 220 (i.e. the number of time input audio samples in block 220) and the rate sampling or sampling frequency. The analysis window 190 used in some embodiments of the present invention thus allows reducing the delay before the delivery of the first and subsequent blocks of audio sub-range values ​​by the filter bank 100.

[0052] Another option of the device 100 is the ability to generate a signal or include some information regarding the analysis window function 190 used to generate the frame 180 or regarding the synthesis window function that should be used to create the synthesis filter bank. The analysis window 190 may thus be in the form of, for example, the synthesis window function used in the synthesis filter bank, but with inverted time or index values.

[0053] Fig. 2a is a block diagram of one embodiment of an apparatus 300 for generating time domain audio samples based on an audio sub-range value block. As described above, an embodiment of the present invention in the form of a device 300 for generating audio signal samples is often referred to as a synthesis filter bank 300 because this device allows the generation of time domain audio signal samples that can in principle be reproduced based on with an audio sub-range value that includes information about the spectrum of the audio signal. The synthesis filter bank 300 thus allows synthesis of time-domain audio signal samples based on audio sub-range values ​​that can be generated, for example, by the corresponding analysis bank filter 100.

[0054] Fig. 2a is a block diagram of a synthesis filter bank 300 including a calculator 310 into which a block 320 of the audio sub-range value (in the frequency domain) is input. The calculator 310 allows the calculation of the frame 330 comprising the time domain intermediate sample sequences based on the audio sub-range values ​​contained in block 320. The frame 330 time-domain intermediate sequence samples in many embodiments of the present invention have a similar block structure as for example a frame of 150 windowed samples of the analysis filter bank

100 shown in Fig. 1. In such cases, the frame 330 includes blocks 340-1,

..., 340-T time domain intermediate samples.

[0055] The sequence of the intermediate time-domain samples of the frame 330, as well as each of the blocks 340 of the intermediate time-domain samples have the order of the time indicated in Fig. 2a by the arrow 350. As a result, the frame 330 contains the earlier intermediate time-domain sample contained in the block 340-T and the latest intermediate time domain sample included in block 340-1, which are respectively the first and last intermediate time domain sample of frame 330. A similar order was also observed for blocks 340. As a result, in some embodiments of the synthesis filter bank the terms "frame" and "sequence" can often be regarded as synonyms.

[0056] The calculator 310 is connected to the synthesis window 360, into which a frame 330 of intermediate time domain samples is inserted. The synthesis window module is adapted to window intermediate time sequence samples using the synthesis window function 370, which is schematically indicated in Fig. 2a. A frame of 380 windowed intermediate time domain samples is provided at the output of the 360 ​​synthesis window module, which may also have a block structure of 390-1, 390-T blocks.

[0057] Frames 330 and 380 may include T blocks 340 and 390, respectively, where 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. In various embodiments of the invention, however, different numbers of blocks may be contained in one of the frames. More specifically, the number of T blocks may in principle be equal to or greater than 3 or equal to or greater than 4, depending on the implementation conditions and the previously described tradeoffs used in embodiments of the present invention including the block structure of the synthesis filter bank 100 and the synthesis filter bank 300.

[0058] The synthesis windowing module 360 ​​is connected to an additive output stage 400 into which a frame of 380 windowed intermediate time domain samples is introduced. The output stage performing the addition with 400 allows processing of windowed intermediate time domain samples to obtain a block of 410 time domain samples. A block of 410 (output) time-domain samples can then, for example, be inserted into subsequent modules for further processing, storage or conversion into audible audio signals.

[0059] A calculator 310 for calculating the time domain sample sequences contained in the frame 330 enables the frequency domain data to be converted to the time domain. The calculator 310 may thus include a frequency / time converter enabling the generation of a signal in the time domain of the spectral representation contained in block 320 of the audio subband samples. As explained in the context of calculator 170 of the analysis filter bank 100 shown in Fig. 1, each of the audio subband values ​​in block 320 corresponds to an audio subband channel having a characteristic center frequency.

[0060] In contrast, the intermediate time-domain samples contained in box 330 generally represent time-domain information. The synthesis window 360 allows and is adapted to window the intermediate sequence of time-domain samples contained in frame 330 using the window synthesis function 370, which is schematically indicated in Fig. 2a.

[0061] As noted above with reference to Figure 1, the synthesis window module 360 ​​also uses the synthesis window function 370, which is obtained by interpolation of a larger window function including a second number of window coefficients. The second number is therefore greater than the first number of window coefficients of the synthesis window function 370 used to window the intermediate time domain samples contained in frame 330.

[0062] The synthesis window function 370 can be obtained, for example, using a synthesis window module 360 ​​or a filter bank 300 (device) performing one of the interpolation schemes described above. The window coefficients of the synthesis window function can be generated, for example, using linear, polynomial or interpolation-based interpolation interpolation. In embodiments of the present invention, interpolation may further be based on the use of subsequent window coefficients of a larger window function. If each of the window coefficients of the larger window function is used exactly once, the window function 370 including the (smaller) first number of window coefficients may include, for example, exactly half the number of window coefficients of the larger window function, if the second number is an even number. In other words, in this case the second number may be twice as large as the first number. When developing embodiments of the present invention, it is also possible to use other interpolation systems and schemes.

[0063] The case of so-called low delay window function will be discussed in more detail below. As noted earlier, embodiments of the present invention are not limited to such window functions, however. Other window functions such as symmetrical window functions may also be used.

[0064] The synthesis window function 370 includes a window coefficient sequence that also includes a first group 420 and a second group 430 window coefficients, as explained above with respect to the window function of analysis 190 comprising the first group 200 and the second group 210 window coefficients.

[0065] The first group 420 of window coefficients of the synthesis window function 370 includes the first portion of successive window coefficients in the window coefficient sequence. Similarly, the second group of 430 window coefficients includes a second portion of consecutive window coefficients in the window coefficient sequence, the first portion having fewer window coefficients than the second portion, and the energy value and the total energy value of the window coefficients in the first portion are greater than the corresponding energy value and the value of the total energy of the window coefficients in the second part. Further features and properties of the synthesis window function 370 may be similar to the corresponding features and properties of the window analysis function 190, which is schematically shown in Figure 1. Consequently, reference is made to the description of the structure of the window function of analysis 190 and the description of the features of the window function with respect to figures 11 to 19, wherein the first group 200 corresponds to the first group 420 and the second group 210 corresponds to the first group 430.

[0066] The parts contained in two groups of window coefficients 420, 430 typically form a set of consecutive and interconnected window coefficients that includes all the window coefficients in the window coefficient sequence of the synthesis window function of the synthesis 370. In many embodiments of the present invention, the analysis window function 190 shown in Fig. Fig. 1 and the synthesis window function 370 shown in Fig. 2a are based on each other. The window function of analysis 190 may, for example, be a time-inverted or version-reverse version of the synthesis window function 370. However, it is also possible to use other relationships between the two window functions 190, 370. It may be advantageous to use the synthesis window function of synthesis window 370, which is associated with the analysis window function 190 used during generation (optionally before modifications) of block 320 of the subband value of the audio signal input into the synthesis filter bank 300 in the synthesis window 360 construction.

[0067] As noted with reference to Fig. 1, the synthesis filter bank 300 shown in Fig. 2a can be optionally adapted so that the input block 320 can include additional signals or additional information regarding window functions. For example, block 320 may include information regarding the analysis window function 190 used to generate block 320 or about the synthesis window function 370 used by the synthesis window module 360. The synthesis filter bank 300 can therefore be adapted to extract individual information and provide it to the synthesis window 360.

[0068] The output stage performing the addition with 400 allows the generation of a block of time-domain samples 410 by processing the windowed intermediate time domain samples contained in the frame 380. In various embodiments of the present invention, the application step with the addition of 400 can include memory allowing temporary storage previously received frames 380 windowed intermediate time domain samples. Depending on the implementation details, the output stage performing overlap with addition of 400 may include, for example, T different memory locations, so that all T frames 380 of windowed intermediate time domain samples can be saved. If required, the output stage performing overlap with addition of 400 may also include a different number of memory locations. In various embodiments of the present invention, the initial step performing an add-on application 400 may independently enable delivery of a block of time-domain samples 410 based on a single frame of 380 time-domain intermediate samples. The implementation of various synthesis filter banks 300 will be described in detail in the following description.

[0069] Fig. 2b illustrates the operating principle of one embodiment of the present invention in the form of a synthesis filter bank 300 in which the generation by synthesis interpolation window 370 is not merely designed to simplify this process.

[0070] The block 320 of the audio subband value is first converted from the frequency domain to the time domain using a calculator 310, which is indicated by arrow 440 in Fig. 2b. The resulting frame 320 of intermediate time domain samples comprising blocks 340-1,., 340 -T intermediate time domain samples are then windowed using a 360 synthesis window module (not shown in Fig. 2b) by multiplying the intermediate time domain samples of the frame 320 by the sequence of synthesis window function coefficients window 370 to obtain a frame of 380 windowed intermediate time domain samples. Frame 380 also includes blocks 340-1,., 340-T windowed intermediate time domain samples, which together form a frame 380 windowed intermediate time domain samples.

[0071] In the embodiment of the synthesis filter bank 300 according to the invention shown in Fig. 2b, the output stage performing overlap with addition of 400 allows zet to generate a block of 419 time domain output samples by adding together for each index value of the audio signal time domain block block 410 intermediate time domain samples of one block of 390 different frames 380. As shown in Fig. 2b The audio signal time block samples of block 410 are obtained by adding together for each index value of the audio signal sample one windowed intermediate sample in the block time domain 390-1 of the frame 380 processed using a 360 synthesis window module and (as described above) corresponding to its intermediate time domain sample of the second block 390-2 of the 380-1 frame processed immediately before frame 280 and stored in the degree memory location initial application with addition of 400. As shown in Fig. 2b, successive corresponding windowed intermediate samples in the time domain of subsequent blocks 390 may be used (e.g. block 390-3 of frame 380-2, block 390-4 of frame 380-3 , block 390-5 of frame 380-4) previously processed using the synthesis filter bank 300. Frames 380-2, 380-3, 380-4 and optionally subsequent frames 380 were processed in earlier stages using the synthesis filter bank 300. Frame 380-2 was processed immediately before frame 380-1, and therefore frame 380-3 was generated directly before frame 380-2 and so on.

[0072] The output stage performing the add-on application 400 used in this embodiment of the invention allows for summing for each index of block 410 (output) time domain samples T different blocks 390-1,., 390-T windowed intermediate time domain samples from T different frames 380, 380-1,., 380 (T-1). In addition to processing the first T blocks, each of the (output) samples in the time domain of block 410 is therefore based on the T different blocks 320 of the subrange values ​​of the audio signal.

[0073] As with the embodiment of the present invention involving the analysis filter bank 100 shown in Fig. 1, due to the form of the synthesis window function 370, the synthesis filter bank 300 provides the ability to rapidly deliver block 410 (output) time domain samples. It is also the result of the synthesis window function 370. Because the first group of 420 window coefficients has a higher energy value and includes a smaller number of window coefficients, the 360 ​​synthesis window module enables the delivery of "full-bodied" frames of 380 windowed samples, if the frame 330 intermediate time-domain samples is filled to such an extent that at least the window coefficients with the first group 420 had an impact on frame 380. The influence of window coefficients from the second group of 430 is smaller due to their lower energy value.

[0074] Therefore, if at first the synthesis filter bank 300 is initialized with a value of 0, the delivery of blocks 410 can in principle begin after the synthesis filter bank 300 receives only a few blocks 320 of the subband values ​​of the audio signal. The synthesis filter bank 300 therefore allows a significant reduction in delay compared to the synthesis filter bank using, for example, the symmetrical synthesis window function.

[0075] As mentioned earlier, the calculators 170 and 310 used in the embodiments of Figures 1 and 2a may be implemented in the form of real numbers operating calculators generating or enabling processing of the real values ​​of the audio subband ranges contained in blocks 180 and 320. In these cases, the calculators can be implemented, for example, in the form of calculators based on real numbers based on harmonic functions such as the sinusoidal function and the cosine function. It is also possible to implement calculators 170 and 310 in the form of calculators operating on complex numbers. In these cases, the calculators can use, for example, complex exponential functions or other complex harmonic functions. The frequency of vibrations with real or complex values ​​usually depends on the index of the audio subband value, which is sometimes also called the band index or the subband index for a given subband. This frequency may also be identical to the center frequency of the corresponding subband or may be dependent on this frequency. For example, the oscillation frequency can be multiplied by a fixed factor, shifted relative to the center frequency of the corresponding subband or depending on a combination of these modifications.

[0076] The calculator 170, 310 operating on complex numbers may be constructed or implemented based on calculators operating on real numbers. In the case of a calculator operating on complex numbers, effective implementation can in principle be used for both parts (sinusoidal and cosine-modulated) of the filter bank representing the real and complex part of the complex value element. This means that it is possible to implement both parts (sinusoidal-modulated and cosine-modulated) for example based on modified DCT-IV and DST-IV structures. In subsequent implementations, it is also possible to use the fast Fourier transform (FFT), which is optionally implemented for both parts (real and complex) of calculators operating on complex numbers using one fast transform

Fourier (FFT), instead of using separate fast Fourier transforms (FFT) for each transformation.

Mathematical description [0077] The following paragraphs show an example of the implementation of the analysis bank filter and the synthesis bank filter with multiple application of 8 blocks on the parts described above, which does not introduce an additional delay and one block into the future, which introduces the same delay as the application of the modified structure discrete sine transform MDCT / modified discrete cine transform MDST. In other words, in the example below, the parameter T is equal to 10.

[0078] First, a description will be given of the complex-value-modulated low-delay analysis filter bank. As shown in Figure 1, the analysis filter bank includes the steps of transforming the analysis windowing carried out by the analysis window module 110 and the analysis modulation performed by the calculator 170. The analysis windowing is based on the equation^fromand._n ~ w (10N - 1 - n) · x_and "For O <n <10 · W, (1) where Zi, n is the windowed sample (of the real value) corresponding to the block index i and the sample index n of the frame 150 shown in Fig. 1. The value xi, n is the input sample over time (with real value) corresponding to the same block index and sample index n. The window function of analysis 190 is represented in equation (1) by its window coefficients with real values ​​in (n), where n is also an index of the window coefficient falling within the range specified in equation (1). As explained above, the parameter N is the number of samples in one block 220, 130, 160, 180.

[0079] Based on the arguments of the analysis window function in (10N-1-n), it can be seen that the analysis window function represents the rotated version of the time-inverted synthesis window function which is currently represented by the window factor w (n).

[0080] The modulation of the analysis carried out in the embodiment shown in Fig. 1 by the calculator 170 is based on two equations (2)

<img file="PL1994530T3_D0001.tif" />

<img file="PL1994530T3_D0002.tif" />

X

<img file="PL1994530T3_D0003.tif" />

(3) for the window coefficient index or the band index k being an integer in the range (4) [0081] The values ​​XReal, l, k, XImag, l, k represent the real part and the complex part of the sub-band value of the audio sub-band with the complex value corresponding to the block index and and the index of the spectral coefficient k of block 180. The parameter does not represent an index option that is equal to n₀ = -N / 2 + 0.5 (5) [0082] As will be described later, the corresponding complex-modulated low-delay synthesis filter bank includes the steps of transforming synthesis modulation, synthesis windowing, and overlay summation.

[0083] Modulation of synthesis is based on an equation

<img file="PL1994530T3_D0004.tif" />

OS n &lt;JO · N

<img file="PL1994530T3_D0005.tif" />

¢ 6) where x '_and,_n is an intermediate sample in the time domain of the frame 330 corresponding to the sample index and the block index i. Also in this case the parameter N is an integer indicating the length of the block 220, 340, 390, 410, which is also determined by the length of the transformation block or - due to the block structure of frames 330, 380 - offset from the previous block. Above also other variables and parameters have been introduced, such as the index of the spectral coefficient k and the number of shifts.

[0084] The synthesis windowing carried out in the embodiment shown in Fig. 2a by the synthesis window 360 is based on the equation = ^{1 for} 0 ί η &lt;10 W, ¢ 7) where Z'i, n is the value of the windowed intermediate sample in the time domain corresponding to the sample index n and the block and frame index 380.

[0085] The stamp for transforming sum with overlap is based on an equation

<img file="PL1994530T3_D0006.tif" />

where outi, n represents the (output) time domain sample corresponding to the sample index n and block index i. Equation (8) therefore represents the overlay adding operation performed by the overlay step performing the addition with 400, as shown in Fig. 2b.

[0086] Embodiments of the present invention are, however, not limited to complex-value modulated low-delay filter banks, enabling audio signal processing using one of these filter banks. It is also possible to implement a low-delay and real-time filter bank for advanced low-delay audio coding. Compared to, for example, equations (2) and (6) for the cosine part, the cosine contribution of analysis and synthesis modulation have a similar structure as that of modified discrete cosine transform (MDCT). Although the method basically allows the extension of the modified discrete cosine transform (MDCT) in both directions of time, only the past extension by E (= T-2) blocks is used, with each T block containing N samples. The frequency factor Xi, k band k block i in the N-channel or N-band filter bank can be described by the equation

2 «-1 / χ \ ,,^{= _2} Σ ⁱⁿ«^IN5^{χ (η)}^c° 4 - + 1 -?) (* +1) 'fi = - £ W

<img file="PL1994530T3_D0007.tif" />

for the index of the spectral coefficient k determined by equation (4). Also in this case n is the sample index, while wa is the analysis window function.

[0087] To preserve the completeness of the information, the above-mentioned mathematical description of the complex-value-modulated filter bank with low delay can be presented in the same summary form as in the case of equation (9), replacing the cosine function with the complex value exponential function. More precisely, for the description and variables given above, equations (1), (2), (3) and (5) can be replaced and expanded using the equation

<img file="PL1994530T3_D0008.tif" />

(10) where, in contrast to equations (2) and (3), the expansion of 8 blocks into the past was replaced by the variable E (= 8).

[0088] The stages of synthesis modulation and synthesis windowing described for the case of complex values ​​using equations (6) and (7) can be summarized for the case of the synthesis filter bank with real values. The frame of 380 windowed intermediate time domain samples, which is also called the demodulated vector, is determined by the equation

<img file="PL1994530T3_D0009.tif" />

(11) where z'i, n is a windowed intermediate time domain sample corresponding to the band index i and the sample index n. The sample index n is also in this case an integer in the range ί η &lt;ί / (2 + £) = Λί Γ (12) while ws (n) is the synthesis window corresponding to the analysis window wa (n) in equation (9). [0089] The step of transforming the overlay summation is then determined by means of an equation

<img file="PL1994530T3_D0010.tif" />

<a name="caption2"></a>J = (_ f + ί) (13) where X'i, n is the reconstructed signal or rather a sample in the block time domain

410 provided by the initial stage performing the application with addition of 400 shown in Fig. 2a.

[0090] For a synthesis filter bank with complex values ​​of 300, equations (6) and (7) can be summarized and generalized in relation to E (= 8) blocks to the path using the equation

<img file="PL1994530T3_D0011.tif" />

where j = V-1 is an imaginary unit. Equation (13) represents the generalized form of equation (8) and also applies to complex values.

[0091] Direct comparison of equation (14) with equation (7) indicates that the window function in (n) in equation (7) is identical to the window function of the synthesis ws (n) in equation (14). As noted above, a similar comparison of equation (10) with the coefficient of the analysis window function wa (n) in equation (1) indicates that the analysis window function is a time-reversed version of the synthesis window function for the case determined by equation (1) ).

[0092] Since the analysis filter bank 100 shown in Fig. 1 and the synthesis filter bank 300 shown in Fig. 2a provide significant improvements with respect to the trade-off between audio delay and processing quality, filter banks 100, 300 are often called small filter banks delay. Their varieties with complex values ​​are sometimes called low-delay complex filter banks, CLDFB for short. Under certain circumstances, the term low-delay complex filter bank (CLDFB) does not only apply to the complex value variant, but also to the real value filter bank.

[0093] As demonstrated above in the description of mathematical foundations, the design used to implement the proposed low-delay filter banks involves the use of techniques resembling modified discrete cosine transform (MDCT) or inverted modified discrete cosine transform (IMDCT) known from the MPEG-4 standard, using extended overlap. Additional overlapping areas can be connected in a block-dependent manner to the left or right of the core of the modified discrete cosine transform (MDCT). In this case, only the extension on the right is used (in the case of the synthesis filter bank), which only covers previous samples, and therefore does not introduce any additional delays.

[0094] Analysis of equations (1), (2) and (14) showed that this processing is very similar to modified discrete cosine transform (MDCT) or inverted modified discrete cosine transform (IMDCT). Thanks to only minor modifications including the modified analysis window function and the synthesis window function, the modified discrete cosine transform (MDCT) or the inverted modified discrete cosine transform (IMDCT) have been expanded to a modulated filter bank that allows for multiple overlap processing and very flexible from a delay point of view. Equations (2) and (3) represent, for example, a complex variety, which was obtained simply by adding sine modulation to a given cosine modulation.

Interpolation [0095] As noted in the context of Figures 1 and 2a, the analysis window 110 and the synthesis window 360 or the corresponding filter banks 100, 300 are adapted to window the respective time frames of samples by multiplying each sample time domain audio signal through individual window coefficients. In other words, each time domain sample is multiplied with a (single) window coefficient, as can be seen, for example, in equations (1), (7), (9), (10), (11) and (14) . As a result, the number of window coefficients of the corresponding window function is usually equal to the number of corresponding time domain audio samples.

[0096] Under certain implementation conditions, however, it may be beneficial to use a window function having a higher second number of window coefficients compared to the current window function having a smaller first number of window coefficients, which is currently used when windowing a corresponding frame or time sequence of audio samples . This may be desirable, for example, when memory requirements are more important than computing performance in a given implementation. Another case in which downsampling may prove to be a more useful solution is the use of the so-called dual frequency technique, which is used, for example, in systems involving replication spectral reconstruction (SBR). The idea of ​​replication spectral reconstruction (SBR) will be discussed in more detail with reference to Fig. 5 and Fig. 6.

[0097] In this case, the analysis window 110 and the synthesis window 360 can be further modified so that the corresponding window function used to window the time-domain audio signal samples delivered to the corresponding window module 110, 360 is obtained by interpolating the window coefficients of a larger window function having a larger second number of window coefficients.

[0098] Interpolation can be performed, for example, in the form of linear, polynomial or interpolation-based interpolation. In the case of, for example, linear interpolation, but also polynomial interpolation and based on compound curves, the corresponding window analysis module 110, 360 can enable interpolation of the window coefficients of the window function used during the window based on two successive window coefficients of the larger window function according to the sequence window coefficients for a larger window function, which allows obtaining one window coefficient of the window function.

[0099] Particularly in the case of an even number of time domain audio samples, the implementation of interpolation described above leads to a significant increase in sound quality. For example, for the even number of NT time-domain audio signal samples in one of the frames 120, 330, without using interpolation, e.g., linear interpolation, adverse aliasing phenomena occur during the further processing of time-domain audio signal samples.

[0100] Fig. 3 is an example of linear interpolation based on a window function (analysis window function or synthesis window function) which is used in the context of frames containing NT / 2 time domain audio signal samples. Due to memory restrictions and other implementation details, the window coefficients of the window function itself are not stored in memory, but the larger window function including NT window coefficients is stored in memory during the process or available using another solution. The upper graph shown in Fig. 3 corresponds to window coefficients c (n) as a function of indexes of window coefficients n in the range from 0 to N T-1.

[0101] Based on the linear interpolation of two successive window coefficients of the window function comprising a greater number of window coefficients, as shown in the upper graph shown in Fig. 3, the interpolated window function is calculated by the equation ci [n] = {(c [2n] + c [2n + l]) for 0 $ η &lt;Ν - T / 2 [0102] Number of interpolated window coefficients c (n ) the window function that is used in the frame comprising NT / 2 time domain audio samples is half the number of window coefficients.

[0103] To show this more clearly, the window coefficients in Fig. 3

450-0, ..., 450-7 are shown in the upper part of Figure 3, corresponding to the coefficients of the window c (0), ..., c (7). Based on these window coefficients and subsequent window coefficients of the window function, the use of equation (15) leads to the coefficients of the window ci (n) of the interpolated window function shown in the bottom of Figure 3. For example, based on the window coefficients 450-2 and 450-3 and the use of equation (15), a window coefficient of 460-1 is obtained, which is indicated in Fig. 3 by arrows 470. Similarly, the window coefficient 460-2 of the interpolated window function is generated based on the window coefficients 450-4 and 450-5 of the window function shown in the upper part of Fig. 3. Fig. 3 shows the generation of further window coefficients ci (n).

[0104] To illustrate the reduction of aliasing possible with interpolated downsampling of a window function, Fig. 4 shows the interpolation of window coefficients in the case of a sine window function which can be used, for example, in modified discrete cosine transform (MDCT). For clarity, the left and right half of the window function have been drawn directly on top of each other. In fig. 4 a simplified version of a sine window containing only 2-4 window coefficients or points for a modified discrete cosine transform (MDCT) with a length of 8 samples is shown.

[0105] Fig. 4 shows four window coefficients 480-1, 480-2, 480-3 and 480-4 of the first half of the sine window and four window coefficients of 490-1, 490-2, 490-2 and 390-4 of the second half of the sine window. The coefficients of the window 490-1,., 490-4 correspond to the indices of the window coefficient 5,., 8. The coefficients of the window 490-1,., 490-4 correspond to the second half of the length of the window function, so that in order to obtain real indexes, add N ' = 4.

[0106] In order to reduce or even eliminate the phenomenon of aliasing in the manner described above, the window coefficient should meet the condition w (n) · (Wl - n) = w (N '+ n) · w (2N'-l - n as closely as possible) )

The more closely the relationship (16) is met, the better the results of reducing or eliminating aliasing.

[0107] Assuming that a new window function comprising half the number of window coefficients is to be determined for the left side of the window function, the following problem arises. Due to the fact that the window function contains an even number of window coefficients (downsampling using even numbers), without using the interpolation scheme shown in Fig. 3 480-1 and 480-3 or 480-2 and 480-4 window coefficients correspond to only one aliasing value of the primary window function or of the primary filter.

[0108] This leads to an imbalance of spectral energy with an asymmetrical arrangement of the center point (center of gravity) of the corresponding window function. When using the interpolation equation (1) for the window factor w (n) shown in Fig. 4, the interpolated values ​​of I1 and I2 meet the aliasing relationship (16) much better, which results in a significant increase in the quality of processed audio data.

[0109] By using an even more refined interpolation scheme, for example an interpolation scheme based on compound curves or the like, it is possible, however, to obtain window coefficients that more closely satisfy equation (16). Linear interpolation is in most cases sufficient, enabling fast and efficient implementation.

[0110] For a typical SBR system using the SBRQMF filter bank (QMF - mirror quadrature filter), it is not necessary to implement a linear or other interpolation scheme because the SBR-QMF prototype filter has an odd number of prototype filter coefficients. This means that the prototype SBR-QMF filter has a maximum value against which downsampling can be implemented, so that the symmetry of the prototype SBR-QMF remains unchanged.

[0111] Figs. 5 and 6 show a possible application of embodiments of the present invention in the form of an analysis filter bank and a synthesis filter bank. One of the important areas of their application are SBR systems and SBR tools (SBR - replicative spectrum reconstruction). Further applications of embodiments of the present invention may, however, relate to other areas in which there is a need for spectral modifications (e.g., gain or equalization modifications), such as object-oriented encoding of spatial audio signals, parametric coding of low-delay stereo signals, low-delay spatial / surround coding , masking frame loss errors, reverberation masking or similar applications.

[0112] The basic idea of ​​replicative spectrum reconstruction (SBR) is to state that in the same signal between the characteristics of the high frequency range of the signal, the so-called high band signal, and the characteristics of the low frequency range of the signal, the so-called low band or low band signal, there is usually a strong correlation. A good approximation of the original high band signal representation can thus be obtained by transposing the low band to high band signal.

[0113] High band reconstruction includes, in addition to transposition, spectral envelope shaping, which includes enhancing the gain. This process is usually controlled by sending a high band spectral envelope of the original input signal. Subsequent control information sent from the encoder allows you to control subsequent synthesis modules, for example, reverse filtering, adding sinusoidal component noise to process audio material in cases where transposition alone may not be sufficient. These parameters include the "high band noise" parameters for adding noise and the "high band tone" parameter for adding a sinusoidal component. This control information is usually called SBR data.

[0114] The Replication Spectrum Reconstruction (SBR) process can be combined using any conventional waveform or codec by using pre-processing at the encoder and post-processing at the decoder. In the process of replicating spectrum reconstruction (SBR), the coding of a portion of the high-frequency audio signal is carried out at a very low calculation cost, while the audio codec is used to encode a portion of the lower frequency audio signal.

[0115] The encoder performs an analysis of the original input signal, and the high band spectral envelope and its characteristics relative to the low band are encoded, after which the obtained SBR data is multiplexed with the bit stream originating from the low band codec. The decoder first performs demiltiplexing of SBR data. The decoding process is usually carried out in stages. First, the core decoder generates a low bandwidth, then the SBR decoder, acting as a post-processing processor, uses the decoded SBR data to control the replication spectrum reconstruction process. In this way, an output signal covering the full bandwidth is obtained.

[0116] In order to achieve the highest coding efficiency and maintain low computational complexity, extended SBR codecs are often implemented in the form of so-called dual frequency systems. Double frequency means that the banded core codec operates at half the external sampling frequency of the audio signal. In contrast, part of the SBR is processed at full sampling frequency.

[0117] Fig. 5 is a schematic block diagram of an SBR 500 system. The SBR 500 system includes, for example, the AAC-LD encoder (AAC-LD - extended low-delay audio codec) 510 and the SBR 520 encoder into which the intended processing audio data. The SBR 520 encoder includes the analysis filter bank 530, which in Figure 5 is shown as a QMF analysis filter bank. The 530 analysis filter bank enables the delivery of audio subband values ​​corresponding to the subranges of audio signals input into the SBR 500 system. The subband values ​​of the audio signal are then introduced into the SBR 540 parameter extraction module, which generates SBR data in the manner described above, including, for example, the high-range spectral envelope, the high-range noise parameter and the high-range key parameter, SBR data are then entered into the AAC encoder -LD 510.

[0118] Fig. 5 shows the AAC-LD 510 encoder as a double frequency encoder. In other words, the 510 encoder operates at half the sampling frequency of the audio data input into the 510 encoder. To enable this, the AAC-LD 510 encoder includes a downsampling stage 550, which optionally may include a low-pass filter to avoid interference caused by, for example, violation of Nyquist-Shannon theorem. The downsampling audio data provided at the output of the downsampling stage 550 is then input into the 560 encoder (analysis filter bank) in the form of a modified discrete cosine transform (MDCT) filter bank. The signals provided by the 560 encoder are then quantized and encoded in the 570 quantization and coding step. The SBR data provided by the SBR 540 secretion module is also encoded to obtain a bit stream, which is then obtained at the output of the AAC-LD 510 encoder. The degree of quantization and encoding 570 can, for example, perform quantization of data according to the hearing characteristics of the human ear.

[0119] The bit stream is then introduced into the AAC-LD 580 decoder being part of the decoder to which the bit stream is transmitted. The AACLD 580 decoder includes a 590 decoding and dequantization step that allows SBR data to be obtained from the bit stream as well as the dequantized or re-quantized low frequency audio data. The low band data is then entered into a synthesis filter bank 600 (inverted modified discrete cosine transform transform (IMDCT) filter bank. Inverted modified discrete cosine transform transform cosine (MDCT) filter bank^-1) 600 converts signals input to the inverse modified discrete cosine transform (IMDCT) stage from the frequency domain to the time domain to obtain a time signal. The time domain signal is then input into the SBR 610 decoder including the analysis filter bank 620, which is shown in Figure 5 in the form of a QMF analysis filter bank.

[0120] The analysis filter bank 620 performs spectral analysis of the time signal input into the analysis filter bank 620 representing the low band. This data is then entered into the high frequency generator 630, which is also called the HF generator. Based on the SBR data provided by the AAC-LD 580 encoder and its degree of decoding and dequantization 590, the HF 630 generator generates high bandwidth based on the low band signals provided by the 620 analysis filter bank. The high and low band signals are then input into a synthesis filter bank 640 that converts the high and low band signals from the frequency domain to the time domain to obtain the time domain audio output signal provided by the SBR 500 system.

[0121] For the sake of completeness, it should be noted that in many cases the SBR 500 system shown in Fig. 5 is not implemented in this way. More specifically, the AAC-LD 510 encoder and the SBR 520 encoder are usually implemented in an encoder that is usually implemented separately from a decoder comprising the AAC-LD 580 decoder and the SBR 610 decoder. In other words, shown in Fig. 5 system 500 essentially represents a combination of two systems, namely an encoder including the above-mentioned 510, 520 encoders and a decoder including the above-mentioned 580, 610 decoders.

[0122] Embodiments of the present invention in the form of analysis filter banks 100 and synthesis filter banks 300 may, for example, be implemented in the system 500 shown in Fig. 5, in lieu of analysis filter bank 530, analysis filter bank 620 and synthesis filter bank 640. In other words in other words, the analysis and synthesis filter banks included in the SBR components of the system 500 can be replaced, for example, with corresponding embodiments of the present invention. Modified discrete cosine transform (MDCT) 560 and inverted modified discrete cosine transform (IMDCT) 600 can also be replaced by low-delay analysis and synthesis filter banks, respectively. In this case, if all the substitutions described have been made, a so-called extended AAC codec (codec = codec) with low latency is obtained.

[0123] The AAC low-delay extended AAC codec (AAC-ELD) combines the low delay of the low-delay extended audio codec (AACLD) with the high coding efficiency of the high-efficiency extended audio codec (HE-AAC) by using replication spectral reconstruction ( SBR) and the Extended Low Delay Audio Codec (AAC-LD). The SBR 610 decoder in this case performs the functions of a processor that performs post-processing, which is used after the 580 core decoder including the full analysis filter bank and the synthesis filter bank 640. The elements of the SBR 610 decoder therefore introduce another decoding delay, which is shown in Fig. 5 shading elements 620, 630, 540.

[0124] In many SBR 500 system implementations, the lower frequency portion or low band typically extends from 0 kHz to 5-15 kHz and is encoded using a wave shape encoder called a core codec. The core codec can be selected, for example, from the MPEG audio codec family. Reconstruction of high frequency or high band parts is also carried out by transforming the low band. The combination of replication spectral reconstruction (SBR) with the core coder is in many cases implemented as a double frequency system in which the AAC encoder / decoder operates at half the sampling frequency of the SBR encoder / decoder.

[0125] Most of the control data is used to represent a spectral envelope that has variable time and frequency resolution to provide control over the Replication Spectrum Reconstruction (SBR) process in the best possible way with the lowest bit rate overhead. Other control data is mainly associated with controlling the high frequency sound / noise ratio.

[0126] As shown in Fig. 5, the output of the AAC 580 decoder used is usually analyzed using the 32-channel QMF 620 filter bank. Then the HF 630 generator module reproduces the high band by inserting into the high band QMF subbands from existing low bandwidth. In addition, reverse filtering is performed based on the subranges and control data obtained from the bit stream (SBR data). The envelope correction module modifies the spectral envelope of the reproduced high band and introduces additional components such as noise and sinusoidal components, which is done in accordance with the control data in the bit stream. Since all operations are performed in the frequency domain (also called the QMF domain or subband ranges), the final step implemented by the decoder 610 is QMF 640 synthesis to preserve the time domain signal. For example, when performing QMF analysis in a encoder using a system of 32 QMF subranges for 1024 samples in the time domain, high frequency reconstruction results in 64 QMF subranges that synthesis allows 2048 samples in the time domain, so a factor is obtained upsampling equal to 2.

[0127] The core encoder delay 510 is further doubled by its operation with a frequency equal to half the original sampling frequency in double frequency mode, which is an additional source of delay in the processes implemented by the AAC-LD encoder and decoder in connection with replication spectral reconstruction (SBR). Later in the description, these sources of delays were analyzed and the delays they introduced were minimized.

[0128] Fig. 6 is a schematic block diagram of the system 500 shown in Fig. 5. Fig. 6 focuses on delay sources in processes implemented by an encoder / decoder that uses coding replication spectral reconstruction (SBR) and low-filter banks delay. Compared to Fig. 5, in Fig. 6 Modified Discrete Cosine Transform (MDCT) 560 and Inverted Modified Discrete Cosine Transform (IMDCT) 600 were replaced by modules with optimized delay, i.e. the so-called Modified Discrete Low Delay Cosine Transform (LD MDCT) 560 'and inverse modified discrete Cosine Transform LD IMDCT) 600 '. The HF 630 generator has also been replaced by a module with an optimized delay of 630 '.

[0129] In addition to the modified low latency cosine transform (LD MDCT) 560 'and inverted modified low latency cosine transform (LD IMDCT) 600' in the system shown in Fig. 6, a modified SBR framing and a modified HF 630 'generator were used. In order to eliminate the delays resulting from the different framing carried out in the core encoder / decoder 500, 600 and the corresponding SBR modules, the SBR framing is adapted to match the frame length to 480 or 512 AAC-LD samples. The variable time grid of the HF 630 generator, which causes the introduction of 384 delay frames, has further been limited in terms of the spread of SBR data in adjacent AC-LD frames. Thus, the only remaining sources of delay in the SBR module are filter banks 530, 620 and 640.

[0130] In the solution shown in Fig. 6, which represents a partial implementation of the AAC-ELD codec, some delay optimization has already been done by applying a low delay filter bank in the AAC-LD core and removing the SBR overlay discussed above. To further optimize the delay, examine the other modules. In fig. 6 the sources of delays in the process implemented by the encoder / decoder using replication spectrum reconstruction (SBR) and low-delay filter banks, here called LD MDCT and LD IMDCT, are presented. Compared to Fig. 5, in Fig. 6 each block represents a delay source, the modules with the optimized delay being shaded. Similar modules have not yet been optimized to reduce latency.

[0131] Fig. 7a is a diagram comprising a C or C ++ pseudocode to illustrate the embodiment of the present invention in the form of an analysis filter bank or a corresponding method for generating audio subband values ​​in audio subband channels. More precisely, Fig. 7a is a schematic diagram of a complex filter bank for 32 bands.

[0132] As noted above, an analysis filter bank is used to divide a time domain signal, for example from a core encoder, into 32 subband signals. In the case of the filter bank, the samples of the band subranges or band subrange values ​​provided at the output of the filter bank have complex values, and therefore are over-sampled with a factor of 2 compared to the real value filter bank. Filtering includes the following steps if the x (n) table contains exactly 320 time-domain samples. The higher the sample index n in the table, the older the samples are.

[0133] After starting performing the method in step S100, the samples in table x (n) are first shifted by 32 positions in step S110. At step S120, the oldest 32 samples are discarded and the new 32 samples are recorded in positions 31 to 0. As seen in Fig. 7a, the received time-domain audio samples are recorded in positions corresponding to an index n decreasing in the range of 31 to 0. This reverses the samples stored in the appropriate frame or vector over time, so that the window function index is reversed to obtain the window function of the analysis based on the (same length) synthesis window function.

[0134] In step S130, the window coefficients ci (j) are obtained by linear interpolation of the coefficients c (j) based on equation (15). The interpolation is based on the block size (block length or number of subband values) equal to N = 64 values ​​and a frame containing T = 10 blocks. The index of the window coefficients of the interpolated window function is therefore in the range of 0 to 319, according to equation (15). Coefficients c (n) are given in the table in Annex 1 to the description. 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 to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplied by the value (-1 )).

[0135] In such cases, the window coefficients in (n) or c (n) can be obtained according to the equation in {n) = w_Taba(n) · s {n) where the sign change function s (n) is &lt;16a)

<img file="PL1994530T3_D0012.tif" />

for n = 0 to 639, and wtable (n) are the values ​​given in the tables in the annexes.

[0136] In order to obtain, for example, the described delay reduction, it is not required, however, to implement window coefficients in accordance with the table in Annex 1. To obtain a delay reduction while maintaining the quality level of processed audio data or to obtain another compromise, the window coefficients c (n) for the index window coefficients n in the range from 0 to 639 must meet one of the sets of conditions given in Annexes 2 to 4. It should further be noted that other window coefficients c (n) may also be used in embodiments of the present invention. Of course, it is also possible to implement other window functions including a number of window coefficients different from 320 or

640, although the tables in Annexes 1 to 4 only apply to window functions that include 640 window coefficients.

[0137] The linear interpolation performed in step S130 allows a significant increase in quality and a reduction or elimination of aliasing effects for a window function including an even number of window coefficients. It should also be noted that the complex number with module 1 is not designated here as j as in equations (1), (2) and (16), but as i = V-1.

[0138] In step S140, the samples of the x (n) table are then multiplied by the coefficients ci (n) of the interpolated window depending on the element.

[0139] In step S150, the windowed samples are added according to the equation given in the diagram in Fig. 7a to form a 64-element table u (n). In step S160, new samples of the subranges of the band or the values ​​of the subranges of the band W (k, l) are calculated according to the matrix operation Mu, where the matrix element M is given by the formula

<img file="PL1994530T3_D0013.tif" />

£ a- &lt;32 0 &lt;n &lt;G4&gt; (Π) where exp () is an exponential function with complex values, and i, as mentioned before, is an imaginary unit. Before looping, the scheme ends with step S170, in which the values ​​of the subband W (k, l) = W [k] [l] can be provided at the output, which corresponds to a sample of the subband 1 in the subband of the index k. In other words, each loop in the diagram shown in fig. 7a allows the creation of 32 subband values ​​with complex values, each of which represents one subband of the filter bank.

[0140] Fig. 7b shows the step S150 of folding the frame 150 windowed time domain audio samples comprising 10 blocks 160-1,., 160-10 windowed time domain audio samples from (n) to the vector u (n) by adding up with five overlaps of two blocks of a frame 150. Folding or retraction is performed depending on the element in such a way that the windowed time-domain audio signal samples corresponding to the same sample index in each of the blocks 160-1, 160-3, 160-5, 160-7 and 160-9 are added to obtain the corresponding value of the first blocks of 650-1 of the vector u (n). Similarly, in step S150, based on blocks 160-2, 160-4, 160-6, 160-8 and 160-10, the corresponding vector elements u (n) are generated in block 160-2.

[0141] A further embodiment of the present invention is in the form of an analysis filter bank that can be implemented as a 64-band low delay and complex value filter bank. The processing of this low-delay and complex value filter bank as the analysis filter bank is essentially similar to the processing of the analysis filter bank described with reference to Fig. 7a. Because of the similarity and basically the same processing as described with reference to fig. 7a, the differences between the complex filter bank of 32 bands and the complex filter bank of 32 subbands shown in Fig. 7a will be presented below.

[0142] In contrast to the analysis filter bank shown in Fig. 7a covering 32 subbands, in the case of a 64-band analysis filter bank 640, the vector frame x (n) includes elements having indices in the range of 0 to 639. Step S110 is therefore modified in such a way that the samples in table x (n) are shifted by 64 positions, with the 64 oldest samples being rejected. In step S120 at positions 63 to 0 instead of 32 new samples, 64 new samples are saved. As shown in Fig. 7c, the received time-domain audio signal samples are recorded in positions corresponding to the index n decreasing in the range of 63 to 0. This causes the inversion of the samples recorded in the appropriate frame or vector, so that already done inversion of the window function index to obtain the window function of analysis based on (same length) synthesis window function.

[0143] Since the window c (n) used for windowing elements of the frame vector x (n) typically includes 640 elements, the step S130 of linear interpolation of window coefficients to obtain the interpolated windows ci (n) can be omitted.

[0144] In step S140, the samples of the table x (n) are multiplied or windowed using the sequence of window coefficients c (n), which in this case are also based on the values ​​given in the table in Annex 1. For window coefficients c (n ) synthesis windowing function windowing or multiplication of the table x (n) by the window c (n) is carried out according to the equation ζ (π) = χ (η) c (n),. _(G) for n = 0,., 639. Also in this case, to achieve a low delay of the window function, the implementation of window coefficients is not required in accordance with the table in Annex 1. In many applications, in order to achieve an acceptable compromise between quality and a significant reduction in delay, the window coefficients must meet one of the sets of conditions given in the tables in Annexes 2 to 4. 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 to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplied by the value (-1 )), according to equations (16a) and (16b).

[0145] Step S150 of the scheme shown in Fig. 7a was replaced by the summation of frame vector samples from (n) according to the equation u (n) = £ (n + j - 126) ₍₁₉&gt;

jeo

For a 128-element array u (n).

[0146] Step S160 of the diagram shown in Fig. 7a has been replaced by a step in which 64 new samples of the band subranges are calculated according to the matrix operation Mu, wherein elements of the matrix M are given by

<img file="PL1994530T3_D0014.tif" />

where exp () is an exponential function with complex values, and and, as mentioned earlier, is an imaginary unit.

[0147] Fig. 7c is a flowchart of an embodiment of the present invention in the form of real-time analysis bank of 32 sub-band channels. The embodiment of Fig. 7c does not differ significantly from the embodiment of Fig. 7a. The main difference between these embodiments is that the step S160 of calculating the new 32 subband values ​​of the complex audio signal band in the embodiment of the invention shown in Fig. 7c is replaced by step S162, in which 32 subband values ​​of the complex signal audio band are calculated according to the matrix operation of Mru, with the elements of the matrix Mr determined by the formula

<img file="PL1994530T3_D0015.tif" />

[0148] As a result, each loop in the scheme allows the creation of 32 subband values ​​with complex values, where W (k, 1) corresponds to a sample of subband 1 in the subband with index k.

[0149] The real-value analysis filter bank can be used, for example, in the low-power SBR system, such as shown in Fig. 5. The low-power SBR system differs from the high-quality SBR tool mainly by using real-value filter banks. This makes it possible to reduce the computational complexity and required computing performance by a factor of 2, so the number of operations per unit of time is generally reduced by a factor of 2, as no imaginary part calculation is required.

[0150] The proposed new filter banks according to the present invention are completely compatible with the low power mode of SBR systems. Thus, the filter banks of the present invention allow SBR systems to operate in either normal or high-quality mode, which uses complex-value filter banks, and in low-power mode, which uses real-value filter banks. A real-value filter bank can be obtained, for example, based on a complex-value filter bank by using only real values ​​(cosine-modulated components) and omitting complex values ​​(sine-modulated components).

[0151] Fig. 8a shows a comparative example of the present invention in the form of a complex synthesis filter bank for 64 channels of subband ranges. As noted above, filtering the synthesis of subband signals processed using replication spectral reconstruction (SBR) is performed using a synthesis filter bank covering 64 subbands. A real-time block of real-time samples is provided at the filter bank output as described in Fig. 1. This process is shown in Fig. 8a, where a comparative example of how to generate time-domain audio samples is also visible. .

[0152] After starting the synthesis filtering in step S200, the following steps are performed, wherein table v includes 1280 samples. At step S210, the samples in table v are shifted by 128 positions, with the oldest 128 samples being rejected. In step S220 64, the new subband values ​​of the complex audio signal band are multiplied by the matrix N, with the elements of the matrix N (k, n) determined by the formula

<img file="PL1994530T3_D0016.tif" />

where exp () is an exponential function with complex values, and i is an imaginary unit. The real part obtained as a result of this operation is recorded in positions 0-127 of table v, as shown in Fig. 8a.

[0153] In step S230, the samples, which are now time domain samples, are obtained from table v according to the equation in Fig. 8a, whereby a 640-element table g (n) is obtained. In step S240, real-time samples of table g are multiplied by the window coefficient c (n) to obtain the table w, with the window coefficients also in this case based on the values ​​given in the table in Annex 1.

[0154] As noted above, it is not required to implement the window coefficients according to the table in Annex 1. In many comparative examples, to achieve the desired low delay of the synthesis filter bank, the window coefficients must meet one of the sets of conditions given in the tables in Annexes 2 to 4. In addition, as described for the analysis filter bank, it is also possible to develop a synthesis filter bank using other window coefficients. 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 to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplied by the value (-1 )), according to equations (16a) and (16b).

[0155] Before the end of one loop of the scheme in step S260, in step S250 64 new output samples are calculated by adding the samples from the table in (n) according to the last step and the scheme given in Fig. 8a. In the scheme shown in Fig. 8a, X [k] [1] (= X (k, 1)) corresponds to the value of audio subband 1 in the subband with index k. As shown in Fig. 8a, 64 new real-time time domain audio samples are received at each new loop.

[0156] The implementation of a complex synthesis filter bank for 64 bands depicted in Fig. 8a does not require the imposition / addition of a buffer covering several memory locations, as described in relation to the embodiment of Fig. 2b. The add-overlay buffer is hidden here in vig vectors, which is calculated based on the values ​​stored in the v vector. The add-overlay buffer is implemented in the construction of these vectors having indexes greater than 128, so these values ​​correspond to values ​​from earlier or later blocks.

[0157] Fig. 8b is a schematic representation of a synthesis filter bank with real values ​​for 64 channel sub-ranges. The real-value synthesis filter bank shown in Fig. 8b can also be used when implementing the low power SBR mode as an appropriate SBR filter bank.

[0158] The diagram shown in Fig. 8b differs from the diagram shown in Fig. 8a mainly by step S222, which is replaced by step S220 shown in Fig. 8a. In step S222 64, the new values ​​of the sub-bands of the real-time audio signal are multiplied by the matrix N, with the elements of matrix No. (k, n) determined by the formula

<img file="PL1994530T3_D0017.tif" />

k

Ο &lt;k &lt;64 Ο ί η &lt;128 f ί²³?

the result of this operation is also recorded in positions 0-127 of table v.

[0159] In addition to these modifications, the diagram of the actual-value synthesis filter bank shown in Fig. 8b for the low-power SBR mode does not differ from that of the complex value synthesis filter bank in Fig. 8a for the high-quality SBR mode.

[0160] Fig. 8c shows a flowchart of the present invention in the form of a downsampling complex synthesis filter bank and a corresponding method that can be used, for example, when implementing the high quality SBR mode. More precisely, the synthesis filter bank shown in Fig. 8c is a complex synthesis filter bank that enables the processing of complex subband values ​​of an audio signal with complex values ​​for 32 channels of subband ranges.

[0161] The downsampling filtering of the synthesis subband signals of the spectrum replication spectrum reconstruction (SBR) process is performed using the 32-channel synthesis filter bank shown in Fig. 8c. After starting the synthesis filtering in step S300, the next steps are performed, with the table v containing 640 real-time samples.

[0162] In step S310, the samples in table v are shifted by 64 positions, with the oldest 64 samples being rejected. In step S320 32, the new values ​​of complex sub-bands or the values ​​of sub-bands of the complex audio signal are multiplied by the matrix N, where elements of the matrix N are given by the formula

<img file="PL1994530T3_D0018.tif" />

MO &lt;η &lt;64, (24) where exp () is an exponential function with complex values, and i is an imaginary unit. The real part obtained as a result of this operation is recorded in positions 0-63 of table v.

[0163] In step S330, samples are obtained from table v according to the equation in Fig. 8c, whereby a 320-element table g is obtained. In step S340, the window coefficients c (n) of the interpolated window function are obtained by linear interpolation of the coefficients c (n) according to equation (15), with the index n also in this case in the range from 0 to 319 (in equation (15) N = 64, T = 10). As shown above, the coefficients of the window function c (n) are based on the values ​​given in the table in Annex 1. As noted above, to obtain a low delay, the implementation of the coefficients of the window c (n) exactly according to the table is not required in Annex 1. It is sufficient that the window coefficients meet one of the sets of conditions given in the tables in Annexes 2 to 4. 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 to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplied by the value (-1 )), according to equations (16a) and (16b). In other embodiments of the present invention, it is of course also possible to use other window functions including different window coefficients c (n).

[0164] In step S350, the array g samples are multiplied by the interpolated window factor c (n) of the interpolated window function to obtain a windowed time domain sample in (n).

[0165] Then, at step S360, new output samples are calculated by adding the samples from the table in (n) according to the last step S360, before performing the final step S370 of the diagram shown in Fig. 8c.

[0166] As noted above, X [k] [1] (= X (k, 1)) corresponds to the value of audio subband 1 in the channel audio subband with index

k. As shown in Fig. 8c, in each new loop, 32 new real-time real-time audio samples are received.

[0167] Fig. 8d shows a schematic of an embodiment of the present invention in the form of a downsampling synthesis filter bank with real values ​​that can be used, for example, in the implementation of the low power SBR mode. The diagram shown in Fig. 8d differs from the diagram shown in Fig. 8c only by the step S320 which in Fig. 8a. replaced by step S322.

[0167] In step S322 32, the new subrange values ​​of the audio signal with real values ​​or the subband values ​​are multiplied by matrix No., wherein elements of matrix No. are given by the formula

<img file="PL1994530T3_D0019.tif" />

the result of this operation is recorded in positions 0-64 of table v.

[0169] Fig. 9a illustrates the implementation of a comparative example in the form of a method corresponding to a complex filter bank for 64 subbands. Fig. 9a shows the implementation in the MATLAB system, where the output y vector and "state" of the vector are obtained. The function specified in the script shown in Fig. 9a is called LDFB80, and a vector x containing new audio samples and the "state" of the vector is introduced into its input. The name LDFB80 is the abbreviation for the low-delay filter bank name in English for 8 blocks extending into the past and 0 blocks extending into the future.

[0170] In the MATLAB programming language, the percent sign (%) indicates comments that are not executed, but are used to comment and explain the source code. In the following description, the individual segments of the source code will be explained in relation to their functions.

[0171] In the S400 code sequence, the buffer represented by the "state" of the vector is updated so that the state content of the vector with indexes 577 to 640 is replaced by the content of the x vector containing the new time domain audio input samples. In the S410 code sequence, the window coefficients of the analysis window function saved in the LDFB80_win variable are sent to the win_ana vector.

[0172] In step S420, where it was assumed that the last samples are set to the right of the buffer, the actual window operation is performed. In step S420, the content of the state of the vector is multiplied (. *) By the elements of the win_ana vector containing the synthesis window function depending on the element. The result of multiplication is saved in the x_win_orig vector.

[0173] In step S430, the contents of the x_win_orig vector is reshaped to create a matrix of 128 x 5 elements, called the stack x. In step S440, the stack character x_stack is changed relative to the second and fourth columns of the x_stack matrix.

[0174] In step S450, the x_stack stack is collapsed or retrieved by adding the x_stack elements with respect to the second index and simultaneously reversing the order of the elements and rearranging the result before saving it again to the x_stack variable.

[0175] In the S460 code segment, a time domain to frequency domain transformation is performed, which is performed by calculating the Fast Fourier Transform (FFT) multiplied by the x_stack stack content element by the complex exponential function into which the ( -i · π · n / 128), where the index is chosen from the range 0 to 127, and the imaginary unit.

[0176] In the S470 code segment, final torsion is performed by determining the variable m = (64 + 1) / 2 and calculating the block including the values ​​of the subranges of the audio signal band in the form of the y vector according to the equation. yW = 2 · temp (k) «exp (- 2i · zr · ((k - 1 + |) · ^))₍₂₆₎ [0177] In the implementation of Fig. 9a, the index k includes an integer range from 1 to 64. The vector y is then output as a vector or block comprising subband values ​​of the audio signal band 180 shown in Fig. 1. The dash located above the second equation of the coefficients (26), as well as above the conj () function of coding the segment S417 in Fig. 9a means a complex complement to the argument of the corresponding complex number.

[0178] In the final segment of the S480 code, the status vector is shifted by 64 elements. The state vector in shifted form can then be input to the LDFB80 function input in the next function loop.

[0179] Fig. 9b shows the implementation of an embodiment of the present invention in a MATLAB system in the form of a method corresponding to a complex analysis bank of filters for 32 subbands. The function specified in the script is therefore called LDFB80_32, which means that the implementation represents a low-delay filter bank for 32 subbands based on an additional overlap of 8 blocks in the past and 0 blocks in the future.

[0180] The implementation of Fig. 9b differs from the implementation of Fig. 9a only with respect to several code sequences, as will be explained later. The code sequences S400, S430, S460, S470 and S480 are again replaced by the corresponding code sequences S400 ', S430', S460 ', S470' and S480 ', mainly taking into account the reduction in the number of sub-band values ​​available on the output of the LDFB80_32 function by a factor of 2. Step S400 'therefore relates to the state of the vector updated with respect to the last 32 positions corresponding to indexes 289 to 320 by input of the corresponding 32 input time-domain audio samples of the new block 220 shown in Fig. 1.

[0181] The main difference between the implementations in Fig. 9a and Fig. 9b, however, appears in the S410 code sequence of Fig. 9a, which in the implementation of Fig. 9b is replaced by the sequence of code S412. The sequence of the S412 code shown in Fig. 9b first includes copying 640 window coefficients comprising the windows stored in the LDFB80_win vector to the local win_ana vector. Then interpolation is performed according to equation (15), during which two successive window coefficients represented by the elements of the win_ana vector are added to each other, divided by 2 and saved again in the win_ana vector.

[0182] The next sequence of S420 code is identical to the sequence of S420 code shown in Fig. 9a, where multiplication (. *) Of windowed values ​​or vector state elements is performed depending on the element by win_ana vector elements containing interpolated window coefficients of the interpolated synthesis window function. The result of multiplication is saved in the x_win_orig vector. The difference between the S420 code sequence shown in Fig. 9b and the corresponding code sequence S420 shown in Fig. 9a is that in the case of Fig. 9b 640 is carried out during windowing, not 320 multiplication operations.

[0183] In the S430 'code sequence, which has been replaced by the S430 code sequence, an x_stack stack is prepared by reforming the x_win_orig vector. However, since the vector X_win_orig contains only 320 elements compared to the corresponding vector shown in Fig. 9a, which contains 640 elements, in this case the x_stack matrix is ​​a 64 · 5 element matrix.

[0184] S440 code sequences including sign change and S540 including stack folding are identical in both implementations of Fig. 9a and Fig.

9b, the only difference is the reduced number of elements (320 compared to 640).

[0185] In the S460 'code sequence, which is replaced by the S460 code sequence, the windowed data is processed using an odd Fourier Fast Transform (FFT), the process being substantially similar to the transformation performed in the S460 code sequence shown in Fig. 9a. Due to the smaller number of output values ​​of the audio sub-ranges, in this case the result of the Fast Fourier Transform (FFT) is introduced into the temp vector, multiplication depending on the element of the x_stack stack elements by the complex exponential function into which the argument (-i is entered) · Π · n / 128), where the index is selected from 0 to 63.

[0186] Then, in the modified S470 'code sequence, final torsion is performed by determining the variable m = (32 + 1) / 2 and generating the output vector y according to equation (26), wherein the index k includes the range of integers from 1 to 32, and the number 128 in the argument of complex exponential function is replaced by 64.

[0187] In the final sequence of S480 'code, the buffer state is shifted by 32 elements in the implementation shown in Fig. 9b, while in the implementation in Fig. 9a the buffer is shifted by 64 elements.

[0188] Fig. 10a is a MATLAB system script illustrating the implementation of a comparative example in the form of a method corresponding to a synthesis filter bank with complex values ​​for 32 subbands. In the script shown in Fig. 10a, the ILDFB80 function is defined, to which the inputs are entered as input parameters, the vector x representing the block 320 of the audio subband values ​​shown in Fig. 2a and the "state" of the state vector. The name ILDFB80 is the abbreviation for the English name of a reverse filter bank with a low delay for 8 blocks extending into the past and 0 blocks extending into the future. This function provides the output of the y vector and a new or re-defined "state" of the state vector, with the y vector corresponding to the block of 410 time domain audio samples shown in Fig. 2a.

[0189] In the S500 code sequence, an initial twist is performed by specifying the variable m = (64 + 1) / 2 and generating the temp vector. The temp elements (n) of the temp vector are given by the formula

<img file="PL1994530T3_D0020.tif" />

Where the dash above the vector element x (n) and the function conj () denote the complex complement, exp () denotes the exponential function of complex values, and is an imaginary unit, and the index ranges from 1 to 64.

[0190] In the S510 code sequence, the temp vector is expanded into a matrix containing the elements of the temp vector in the first column, and in the second column a complex complement of the temp vector inverted with respect to the order of the elements determined by the vector index. In the S510 code sequence, therefore, the odd symmetry of the temp matrix is ​​determined based on the temp vector.

[0191] In the code sequence S520, a fast Fourier transform (FFT) is performed based on a temperature matrix. In this code sequence, the real part multiplies depending on the element elements of the result of the fast Fourier transform (FFT) of the temperature matrix by the exponential function into which it is introduced argument (-i · π / 128), where index n is selected from 0 to 127, is written in the y_knl vector.

[0192] In the code sequence S530, a data extension and alternating sign change are created. To obtain this result, the order of the y_knl vector elements is reversed and at the same time a sign change is carried out. Next, the tmp matrix containing the first, third and fifth columns of the y_knl vector is determined, wherein the second and fourth columns contain the changed sign y_knl vector.

[0193] In the code sequence S540, the window coefficients stored in the LDFB80_win vector are copied to the win_ana vector. Next, the synthesis window coefficients are determined based on the analysis window coefficients saved in the win_ana vector by generating a time-reversed version of the analysis window function according to the equation win _ syn (n) = win _ ana (N · T - n) (28) where N · T is the total number of window coefficients, and n is the index of window coefficients.

[0194] In the S550 code sequence, the tmp vector is processed using the synthesis window by multiplication depending on the vector element by a synthesis window function. In the S560 code sequence, the buffer is updated by inserting state vector elements with indexes 577 to 640 to 0 and adding the contents of the tmp vector window to the state vector state.

[0195] In the S570 code sequence, the output y vector sample time-domain audio signal is obtained based on the state vector by selecting state vector elements, wherein it is done by selecting state vector elements with indexes 1 to 64 .

[0196] In the code sequence S580, which is the final code sequence of the function shown in Fig. 10a, the state of the state vector is shifted by 64 elements, so that elements with indexes 65 to 640 are copied to the first 576 elements of the state vector.

[0197] Fig. 10b is a MATLAB script illustrating an embodiment of the present invention in the form of a complex synthesis filter bank for 32 band sub-ranges. In the script shown in Fig. 10a a function called ILDFB80_32 is defined, which indicates a function that is an inverted filter bank with a low delay for 32 bands, with 8 blocks superimposed from the past and 0 blocks superimposed from the future.

[0198] As discussed with reference to the comparison of the implementations in Fig. 9a and Fig. 9b, the implementation of the script shown in Fig. 10b is also closely related to the implementation of the synthesis filter bank for the 64 sub-ranges of the band shown in Fig. 10a. As a result, the same vectors are introduced into the function and the same vectors are provided at the output of the function, but they only contain half the number of elements compared to the implementation shown in Fig. 10a. The implementation of the 32-band synthesis filter bank for 32 bands differs from the version for the 64 sub-bands shown in Fig. 10 mainly in two aspects. The code sequences S510, S520, S53b, S560, S570 and S580 were replaced by code sequences in which the number of addressed elements and the number of parameters associated with the elements were divided by 2. The S540 code sequence for generating the synthesis window function has also been replaced by the S542 code sequence in which the synthesis window function is generated by linear interpolation of the synthesis window function according to equation (15).

[0199] In the S500 'code sequence, which replaces the S500 code sequence, the variable m equal to m = (32 + 1) / 2 and the temperature vector defined according to equation (27) are determined, with the index n covering only the range from 1 to 32, while in the argument of the exponential function factor 1/128 is replaced by factor 1/64.

[0200] Similarly, in the S510 'code sequence, which replaces the S510 code sequence, the index range only includes the temp vector containing 32 elements. In other words, the index only includes values ​​in the range of 1 to 32. Similarly, in the code sequence S520 ', which replaces the sequence of code S520, the argument of the exponential function is replaced by (-i · π · n / 64), where the index n is selected range from 0 to 63. In the construction of the S530 'code sequence, the range encompassed by the index has also been reduced by a factor of 2 compared to the S530 code sequence.

[0201] In the code sequence S542, which replaces the code sequence S540 shown in Fig. 10a, the window function stored in the LDFB80_win vector is also copied to the win_ana vector and the time-reversed version of win_syn is generated according to equation (28). The code sequence of S542 in the implementation shown in Fig. 10b, however, further includes an interpolation step according to equation (15), during which for each element of the again defined win_syn vector including the window coefficients of the synthesis window function linear interpolation of two successive window coefficients of the original window synthesis window function is performed.

[0202] The S550 code sequence comprising processing the tmp vector using the window and replacing the tmp elements with their windowed versions is identical in code view to the corresponding code sequences in Fig. 10a and Fig. 10b. However, due to the smaller size of the tmp vector, in the implementation shown in Fig. 10b, twice the number of multiplications is carried out.

[0203] In the construction of the S560 ', S570' and S580 'code sequences, which replaced the S560, S570 and S580 code sequences, respectively, indexes 640 and 64 were also replaced by indexes 320 and 32, respectively. These three terminal code sequences are therefore different from the sequences code used in the implementation of Fig. 10a only by the length of the states of the tmp and y vectors.

[0204] In the embodiments of the invention presented so far, the analysis window module and the synthesis window module are adapted to window the respective time-domain samples contained in their respective frames by multiplying these samples depending on the element by window coefficients of the window function.

[0205] Before providing a more detailed description of the window function that can be used, for example, as a synthesis window function or the window function of the time-reversed analysis, the advantages of the present invention will be described in more detail, especially from the point of view of their implementation in tool design SBR or the system shown in Figs. 5 and 6.

[0206] In addition to other advantages, embodiments of the present invention and systems comprising more than one embodiment of the present invention can provide a significant reduction in latency compared to other filter banks. However, the low delay will be described in more detail with reference to Fig. 13 and Fig. 14. One important aspect in this context is that the length of the window function, and in other words the number of window coefficients used to process the frame or block of samples in the time domain, is independent of delay.

[0207] Embodiments of the present invention also have another advantage in increasing the quality of (reconstructed) audio data. Given the number of window coefficients, the interpolation used in embodiments of the present invention provides a significant reduction in aliasing compared to other schemes for reducing it.

[0208] As will be described in more detail below with reference to Figs. 17 and 18, from the psychoacoustic point of view, the present invention often uses the time masking properties of the human ear better than is the case with other filter banks. As will be described in more detail below with reference to Figs. 15, 16 and 19, embodiments of the present invention provide an excellent frequency response.

[0209] With many embodiments of the filter banks of the present invention, it is also possible to achieve perfect reconstruction if the analysis filter bank and the synthesis filter bank are connected to each other. In other words, the embodiments of the present invention not only allow an inaudible difference between the output and input signals introduced into the set of interconnected analysis filter banks and the synthesis filter bank, but (apart from quantization errors, rounding effects in calculations, and other effects caused by the need to discretize ) the output signal can be identical to the input signal.

[0210] The integration of filter banks of the present invention in an SBR module is simple. Because SBR modules typically operate in dual frequency mode, the low-delay complex-value filter banks of the present invention allow for excellent reconstruction in single-frequency mode, while typical SBM QMF filter banks allow for reconstruction with only similar parameters. In the 3256 dual frequency mode, the bandwidth version of the impulse response is obtained by linear interpolation, also called downsampling of two adjacent window coefficients of the 64-band impulse response or window function, as described with reference to Figure 3.

[0211] In the case of implementing a complex filter bank, it is possible to achieve a significant reduction in the delay introduced during the analysis (or synthesis) of the sampled filter banks in which the sampling or processing frequency corresponds to the cutoff frequency according to NyquistShannon's theorem. In the case of implementation of a real-value filter bank, it is possible to achieve an effective implementation using optimized algorithms, for example, as shown in the context of the MATLAB scripts shown in Fig. 9 and Fig. 10. These implementations can be used, for example, in the low-power mode of the SBR tool as described with reference to Fig. 5 and Fig. 6.

[0212] As described with reference to Figs. 5 and 6, it is possible with the SBR system to further reduce the delay by utilizing the implementation of the low-delay complex-value filter bank of the present invention. As described above, in the SBR decoder shown in Fig. 5, the QMF 620 filter bank is replaced by the low-delay complex value filter bank (CLDFB) of the present invention. This change can be performed computationally by maintaining the number of bands (64), the length of the impulse response (640) and the use of complex value modulation. The delay achieved with this tool is minimized to the point of achieving a sufficiently low total delay to allow two-way communication while maintaining an acceptable level of quality.

[0213] Compared to, for example, a system employing modified discrete cosine transform (MDCT) or modified discrete sine transform (MDST) to create a complex value MDCT system, embodiments of the present invention provide a better frequency response. Compared to, for example, the QMF filter bank currently used in SBR MPEG-4 systems, a system comprising one or more filter banks according to the present invention provides significantly less delay.

[0214] Even compared to the low delay QMF filter bank, embodiments of the present invention provide the advantage of excellent reconstruction combined with less delay. The advantages of perfect reconstruction compared to near-perfect reconstruction obtained using QMF filter banks are as follows. For near-perfect reconstruction, a large damping band must be used to suppress aliasing to a sufficiently low level. This limits the possibility of obtaining a very low delay in the filter design. In contrast, the use of an embodiment of the present invention now creates the possibility of independent filter development, so that it is not necessary to use a large attenuation band to suppress aliasing to a sufficiently low level. The attenuation band must be small enough to allow aliasing to be reduced to the extent that the desired signal processing can be used. Thus, in the filter design it is possible to achieve a better compromise regarding a lower level of delays.

[0215] Fig. 11 shows a comparison of a window function 700, which can be used, for example, in embodiments of the present invention, with a sine function 710. A window function 700, which can also be called a CMLDFB "synthesis" window (CMLDFB = low filter bank complex values), includes 640 window coefficients based on the values ​​given in the table in Annex 1. Given the size of the windowed functions, it should be noted that the general gain or damping factors used to correct the amplitude of the windowed signal are not included below. For example, window functions can be normalized relative 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 the window coefficients. For comparison, the sine window function 710 is specified only for 128 samples and can, for example, be used in the case of modified discrete cosine transform (MDCT) or modified discrete sine transform (MDST).

[0216] Depending on the implementation details, in order to obtain window coefficients based on the values ​​given in the tables in Annexes 1 and 3, however, additional changes to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplied by value (-1)) according to equations (16a) and (16b).

[0217] Before discussing the differences between the two window functions 700, 710, it should be noted that both window functions only contain window coefficients with real values. In both cases, the absolute value of the window coefficient corresponding to the index n = 0 is also less than 0.1. For the CMLDFB 700 window, this value is even less than 0.02.

[0218] Considering the two window functions 700, 710 with respect to their definition sets, several significant differences are evident. While the sine window function 710 is symmetrical, window function 700 exhibits asymmetrical behavior. In other words, the sine window function is symmetrical, because not for all real numbers n there is a real value for which window function 710 is specified for (n0 + n) and (n0-n), and the relationship

My - «ϊ = My + nj ₍₂₉₎ is satisfied with the desired margin (ε&gt; 0; the absolute value of the difference considering the two sides of the equation (29) is less than or equal to ε), where in (n) is the window coefficient corresponding to the index n. In the case of a sine window, the corresponding index is not located exactly in the middle of the two highest window coefficients. In other words, for the sine window 710 the index is not equal to 63.5. The sine window function is specified for indexes n = 0,., 127.

[0219] In contrast, the window function 700 is defined for a set of indexes n = 0,., 639. The window function 700 is purely asymmetrical in the sense that for all real numbers n0 there is at least one real number such that ( n0 + n) and (n0-n) belong to the set of window function definitions, and the inequality

My - * My + n) ₍₃₀₎ maintains (basically intentionally) a definable margin (ε&gt; 0; the absolute value of the difference considering the two sides of the equation (29) is greater or equal to ε), where also in (n) the window coefficient corresponding to the index n.

[0220] Further differences between the two window functions, both regarding blocks with a size of N = 64 samples, are that the maximum value of window function 700 is greater than 1 and is obtained for indexes in the range

<img file="PL1994530T3_D0021.tif" />

for the synthesis window. For the window function 700 shown in Fig. 11, the maximum value obtained is greater than 1.04 and is obtained for the sample index n = 77. In contrast, the maximum values ​​of the sine function 710 are less than or equal to 1 and are obtained for n = 63 in = 64.

[0221] Also, however, the window function 700 obtains a value close to 1 for sample indexes equal to about n = N. More precisely, the absolute value or the value of the window coefficient w (N-1) corresponding to the index n = N-1 is less than 1 while the absolute value or value of the window coefficient in (N) corresponding to the index n = N is greater than 1. In some embodiments of the present invention, these two window coefficients satisfy the equation

0.99 &lt;r / (W - 1) &lt;1.0 1.0 &lt;tf (w) &lt;1.01 (32) which results in the optimization of the audio quality of the filter banks according to the present invention. In many cases, it is desirable that the window coefficient w (0) including the absolute value be as small as possible. In this case the determinant of the window coefficients

<img file="PL1994530T3_D0022.tif" />

it should be as close to 1 as possible, thanks to which it is possible to achieve optimized sound quality in relation to given parameters. However, it is possible to freely choose the determinant mark, which is determined by equation (33). If the window coefficient in (0) is less than or approximately equal to 0, the result of (N1) · in (N) or its absolute values ​​should be as close as possible to +/- 1. In this case, the factor w (2N-1) can in principle be chosen freely. Equation (33) is the result of using the zero-delay matrix technique described in the publication "New Framework for Modulated Perfect Reconstruction Filter Banks" by GDT Schuller and MJT Smith, IEEE Transactions on Signal Processing, vol. 44, No. 8, August 1996.

[0222] As will be explained in more detail with reference to Fig. 13, the window coefficients corresponding to the N-1 and N indexes are furthermore in the middle of the modulation core, and therefore correspond to a sample of approximately 1.0, which coincides with the delay of the filter bank defined by the prototype filter function or window function.

[0223] The window synthesis window 700 shown in Fig. 11 further exhibits an oscillating nature with closely monotonically increasing window coefficients, beginning with the window coefficient of the window coefficient sequence corresponding to the index (n = 0) used to window the last audio signal in the time domain and ending on the window coefficient having the largest absolute value of all window coefficients of the synthesis window function 700. Of course, in the case of the inverted window function of analysis, the oscillating nature includes strictly monotonically decreasing window coefficients, starting from the window coefficient having the largest absolute value of all window coefficients of the corresponding window function (inverted), and ending with the window coefficients of the sequence of window coefficients corresponding to the index (n = 639) used to window the last sample of the audio signal in the time domain.

[0224] As a consequence of its oscillating nature, the development of the synthesis window function 700 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 less than 0.03, followed by obtaining a value of about 1 at the index n = N, obtaining a maximum value greater than 1.04 at the index according to equation (31), obtaining another value of approximately 1 at index n = 90 and 91, the first change of the sign carried out at index values ​​of n = 162 in = 163, obtaining a minimum value of less than -0.1 or -0.12755 at an index of approximately n = 3N and the next sign change at index values ​​n = 284 and n = 285. The synthesis window function of 700 may, however, include subsequent sign changes at subsequent index values ​​n. When comparing the window coefficients with the values ​​given in the tables in Annexes 1 and 3, however, additional changes to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 (multiplication by the value (-1)) should be taken into account, according to equations (16a ) and (16b).

[0225] The oscillatory nature of the synthesis window function 700 is similar to strongly damped oscillations, as illustrated by a maximum value of approximately 1.04 and a minimum value of approximately -0.12. As a result, over 50% of window coefficients have absolute values ​​less than or equal to 0.1. As noted with respect to the embodiments of the invention shown in Fig. 1 and Fig. 2a, the development of the window function includes the first group 420 (or 200) and the second group 430 (or 210), wherein the first group 420 comprises the first part of the subsequent window coefficients, and the second group 430 comprises the second part of the subsequent window coefficients. As described earlier in the description, the window coefficient sequence only includes the first group of 420 window coefficients and the second group of 430 window coefficients, with the first group of 420 window coefficients covering exactly the sequence of the first consecutive window coefficients, and the second group of 430 window coefficients includes exactly the second part of the next window coefficients. The terms first group 420 and first part of the window coefficients as well as the terms second group 430 and the second part of the window coefficients can therefore be used interchangeably.

[0226] More than 50% of window coefficients having absolute values ​​less than or equal to 0.1 are contained in the second group or second part of 430 window coefficients, which is a consequence of the oscillating with strong damping character of the synthesis window function 700. More than 5.0% of the window coefficients contained in the second group or second part 430, the window coefficient further has an absolute value less than or equal to 0.01.

[0227] The first portion 420 of window coefficients comprises less than one-third of all window coefficients of the window coefficient sequence. The second portion 430 of window coefficients thus comprises over two-thirds of all window coefficients. When the total number of T blocks to be processed in one of the 120, 150, 330, 380 frames is greater than four blocks, the first part usually includes 3/2 · N window coefficients, where N is the number of time domain samples contained in block. The second part therefore includes the remaining window coefficients or, more precisely, (T-3/2) N window coefficients. In the one depicted in fig. 11 in the case where T = 10 blocks, the first part includes 3/2 · N window coefficients, while the second part includes 8.5 · N window coefficients. For a block size of N = 64 audio samples per block, the first part has 96 window coefficients and the second part has 544 window coefficients. Shown in fig. 11 synthesis window function 700 obtains a value of approximately 0.96 at the border between the first part and the second part corresponding to an index of about n = 95 or 96.

[0228] In addition to the number of window coefficients contained in the first part 420 and the second part 430, there is also a significant difference in the energy value and the total energy value of the corresponding coefficients. The energy value is determined by the equation^Ε = Σ &lt;, 041 η » ^L where in (n) is the window coefficient, and the index n used to calculate the sum in equation (34) corresponds to the indexes of the respective parts 420, 430, the entire set of window coefficients or any other set of window coefficients to which the corresponding energy values ​​E correspond. window coefficients, the energy value of the first portion 420 is equal to or greater than 2/3 of the total energy value of all window coefficients. The energy value of the second part 430 is therefore less than or equal to 1/3 of the total energy value of all window coefficients.

[0229] The energy value of the first window portion 420 of the window function coefficients 700 is about 55.85, while the energy value of the second part 430 is about 22.81. The total energy value of all window coefficients of the window function 700 is about 78.03, so the energy value of the first part 420 of the window coefficients is about 71.6% of the total energy value, while the energy value of the second part 430 is about 28.4% of the total energy value of all window coefficients.

[0230] Equation (34) can of course be presented in the normalized version by dividing the energy value E by the normalizing factor E0, which can in principle be in the form of any energy value. The normalizing factor E0 may be, for example, the total energy value of all window coefficients of the window coefficient sequence calculated using equation (34).

[0231] Based on the absolute values ​​of the window coefficients or the energy values ​​of the corresponding window coefficients, it is possible to determine the midpoint or "center of gravity" of the window coefficient sequence. The center of gravity or center point of the window coefficient sequence is a real number and is usually located in the index range belonging to the first part 420 of the window coefficients. In the case where the corresponding frames contain more than four blocks of time-domain audio samples (T&gt; 4), the center of gravity nca determined on the basis of the absolute values ​​of the window coefficients or the center of gravity nce determined on the basis of the energy values ​​of the window coefficients shall be less than 3 / 2 · N. In other words, when using T = 10 blocks per frame, the center of gravity is located within the index range corresponding to the first part 200.

[0232] The center of gravity nca determined based on the absolute values ​​of the window coefficients in (n) is calculated according to the equation

n.

in τ-Ł

Σⁿ k (ⁿ) l (35) and the center of gravity nce determined based on the absolute values ​​of the window coefficients in (n) is calculated according to the equation n,

Σ ⁿ kW

Ν-Γ-1

<img file="PL1994530T3_D0023.tif" />

Σ kW (36) where N and T are positive integers specifying the number of time-domain audio samples per block and the number of blocks in the frame, respectively. The centers of gravity calculated in accordance with equations (35) and (36) can of course also be determined using a limited set of window coefficients, by appropriately modifying the limits for calculating sums. [0233] For the window function 700 shown in Fig. 1, the center of gravity nca determined based on the absolute values ​​of the window coefficients in (n) has the value n_ca ~ 87.75, and the center of gravity n_ce determined on the basis of the absolute values ​​of the window coefficients in (n) has the value n_ce ~ 80.04. Since the first part 200 of the window coefficients of the window function 700 includes 96 (= 3/2 · N; N = 64) window coefficients, both midpoints are located in the first part of the window coefficients as described above.

[0234] The window coefficients in (n) a window function 700 are based on the values ​​given in the table in Annex 1. To achieve the low delay of the filter bank described above, however, it is not required to implement the window function exactly according to the table in Annex 1. In many applications, it is more than enough that the window coefficients of the window function comprising 640 window coefficients meet any of the relationships or equations given in the tables in Annexes 2 to 4. The window coefficients or filter coefficients given in the table in Annex 1 are preferred values, which in some implementations can be modified according to equations (16a) and (16b). As noted, however, in the following tables in the following annexes, preferred values ​​may differ by a second, third, fourth or fifth digit after the decimal point, so that the resulting filters or window functions still have the advantages of the present invention. 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 to the sign of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be taken into account (multiplied by the value (-1 )), according to equations (16a) and (16b).

[0235] Of course, in embodiments of the present invention, it is possible to specify and use other window functions including various numbers of window coefficients. In this context, it should be noted that the number of time-domain audio samples per block and number of blocks in the frame, as well as the arrangement of blocks relative to past and future samples, can vary widely.

[0236] Fig. 12 is a comparison of the low delay CMLDFB complex window bank (CMLDFB windows) 700 shown in Fig. 11 and the primary prototype filter SBR QMF 720, used for example in the SBR tool in the MPEG standard. As seen in Fig. 11, the CMLDFB 700 window also in this case is in the form of a synthesis window according to one embodiment of the present invention.

[0237] While the window function 700 according to embodiments of the present invention is strictly asymmetrical, as described in relation to equation (30), the primary prototype filter SBR QMF 720 is symmetrical with respect to the indexes n = 319 and 320, if the window function 700 and the filter prototype SBR QMF 720 were determined based on 640 indexes. In other words, for the SBR QMF 720 prototype filter, the "index value" not representing the symmetry center index is no = 319.5, according to equation (29).

[0238] Due to the symmetry of the SBR QMF 720 prototype filter, also the midpoint nca and nce determined according to equations (35) and (36) respectively are identical to the center of symmetry no. The energy value of the SBR QMF 720 prototype filter is 64.00, because the prototype filter is an orthogonal filter. In contrast, the strictly asymmetrical window function 700 has an energy value of 78.0327, as described above.

[0239] In the following paragraphs of the description, SBR systems described with reference to Figs. 6 and 6 will be considered, in which the SBR 610 decoder includes the implementation of the present invention in the form of an analysis filter bank constituting the filter bank 620 and an embodiment of the present invention in the form of a synthesis filter bank constituting a synthesis filter bank 640. As will be explained in more detail below, the total delay of the analysis filter bank of the present invention, including the window function 700 shown in Fig. 11 and Fig. 12, is 127 samples, while the SBR tool using the primary SBR QMF prototype filter introduces delay of 640 samples.

[0240] Replacement of QMF filter banks in the SBR module, for example in the SBR decoder, with a complex delay low-delay filter bank (CLDFB) results in a reduction of the delay from 42 ms to 31.3 ms without any reduction in sound quality or increasing computational complexity, New filter banks support the standard SBR mode (high quality mode) and the low power mode using only real value filter banks, as described in the description of embodiments of the present invention shown in Figs. 7 to 10.

[0241] Low latency is extremely important especially for applications related to telecommunications and two-way communication. The extended low-AAC audio codec allows telecommunications applications to achieve a sufficiently low delay of 42 ms, but its algorithmic delay is still greater compared to the delay introduced by the low-delay AAC codec capable of achieving a delay of about 20 ms, as well as other codecs for telecommunications applications, In the SBR 610 decoder, the QMF analysis and synthesis steps still introduce a 12 ms reconstruction delay. A promising way to reduce this delay is to use low-delay filter bank technology according to individual embodiments of the present invention and replace the currently used QMF filter banks with the corresponding low-delay versions according to individual embodiments of the present invention. In other words, a further delay reduction can be obtained simply by replacing the usual filter banks used in the SBR 610 module with a low delay complex value filter bank according to individual embodiments of the present invention.

[0242] The new filter banks of the present invention, also called CLDFB modules, intended for use in the SBR 610 module, are designed to be as similar as possible to the originally used QMF filter banks. This includes, for example, the use of 64 sub-bands or bands, the same length of impulse responses, and ensuring compatibility with dual-frequency modes that are used in SBR systems.

[0243] Fig. 13 shows a comparison of the shape of a low delay filter bank with complex values ​​CMLDFB 700 according to the present invention and the primary prototype filter SBR QMF 720. Also presented here is the delay of modulated filter banks, which can be determined by analysis of the overlap delay introduced by the prototype filter or window function in addition to the framing delay of the modulation core having in the DCT-IV system the length of N samples. The situation in Fig. 13 once again relates to the case of the synthesis filter bank. The window function 700 and the prototype filter function 720 also show impulse responses of prototype synthesis filters comprising two filter banks.

[0244] Regarding the analysis of the delay introduced by the SBR QMF filter bank and the proposed CMLDFB filter bank according to the present invention, the delay during analysis and synthesis is only introduced when applied to the right or left side of the modulation core.

[0245] For both filter banks, the modulation core is based on the DCT-IV system introducing a delay of 64 samples, which is indicated in Figure 13 as a delay of 750. In the case of the SBR QMF 720 prototype filter, due to its symmetry, the delay of the modulation core 750 is symmetrical about the center of gravity or midpoint of the corresponding 720 prototype filter function, as indicated in Fig. 13. The reason for this behavior is that the SBR QMF filter bank buffer needs to be filled to such an extent that the prototype filter function 720 has the most significant share in terms of the corresponding energy values ​​of the prototype filter used during processing. Due to the shape of the prototype filter function 720, it is required to fill the buffer at least to the center of gravity or midpoint of the appropriate prototype filter function.

[0246] To illustrate this more precisely, starting with the full buffer initialization of the corresponding SBR QMF filter bank, the buffer must be filled to such a point that the data processing is in the form of significant data processing, which requires a significant share of the corresponding window or prototype function filter function, For the SBR QMF prototype filter function, the symmetrical shape of the 720 prototype filter introduces a delay of the order of the center of gravity or the midpoint of the prototype filter function.

[0247] However, since there is always a delay introduced by the DCT-IV modulation core for N = 64 samples, and the system also includes a delay of one block, it can be seen that the QMF SBR synthesis prototype introduces an application delay of 288 samples.

[0248] As noted above, for the synthesis filter banks associated with Fig. 13, the delay is introduced by additional overlay of the left side 760, while overlay of the right side 770 applies to past samples, and therefore for the synthesis filter banks does not introduce additional delay.

[0249] In contrast, in the case of the CLDFB filter bank of the present invention, after the buffer has been fully initialized, the synthesis filter bank and the analysis filter bank allow "important" data to be delivered earlier than it is the case with the SBR QMF filter bank, which is associated with the shape of the window function. In other words, due to the shape of the window function, the analysis and synthesis of 700 samples processed by window functions previously show a significant share. As a result, the synthesis prototype or window synthesis window of the CLDFB filter bank introduces an application delay of only 32 samples, taking into account the delay already introduced by the modulation core 750. The first portion 420 or first group 420 of window coefficients of the window function 700 according to the present invention includes in a preferred embodiment 96 window coefficients, which corresponds to the delay introduced by applying on the left side 760 together with the delay of the modulation core 750.

[0250] The analysis filter bank and prototype analysis function introduce the same delay. The reason is that the analysis filter bank is based on a time-reversed version of the synthesis window function or prototype function. Thus, for the original QMF prototype filter, a delay of 288 samples is also introduced, while the analysis filter bank of the present invention provides a delay of only 32 samples.

[0251] The table in Fig. 14a provides an overview of the delays of the various modification stages, assuming a frame length of 480 samples and a sampling frequency of 48 kHz. In the standard configuration including the AAC-LD codec with the standard SBR tool, the MDCT and IMDCT filter banks operating in dual frequency mode cause a 40 ms delay. The QMF tool itself also introduces a 12 ms delay. Due to SBR overlap, a further delay of 8 ms is generated, so the total delay of this codec is about 60 ms.

[0252] Compared to the above, the AAC-ELD codec comprising low delay versions of modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) generates a double frequency mode delay of 30 ms. The SBR tool's original QMF prototype filter using the complex low-delay filter bank of the present invention results in a delay of only 1 ms, and for comparison the original QMF tool causes a delay of 12 ms. By avoiding SBR overlap, it is possible to completely eliminate the additional 8 ms overlap introduced by directly connecting the AAC-LD codec and the SBR tool. The extended audio codec with low AAC delay thus allows for a total calculation delay of 31 ms compared to the delay described above by the direct connection described above, which is 60 ms. Thus, it can be seen that the combination of the delay reduction methods described above actually enables a total delay of 29 ms to be reduced.

[0253] The table in Fig. 14b gives another overview of the total codec delays introduced by the original and disclosed version of the system shown in Figs. 5 and 6. The data and values ​​in Fig. 14b are given using a frame length of 480 samples and a sampling frequency of 48 kHz. Due to the double frequency mode used in the SBR system discussed above with reference to Fig. 5 and Fig. 6, the core encoder efficiently operates with a sampling frequency of 24 kHz. Since the modulation core framing delay of 64 samples is introduced by the core encoder, it can be subtracted from the single delay values ​​of the two filter banks shown in relation to Fig. 13.

[0254] In the table of Fig. 14b, it can be seen that a delay of the extended AAC low coded delay audio codec including low delay versions of modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) is possible. While a total calculation delay of 42 ms is only possible by using the low delay version of the modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) as well as the original QMF filter banks, the use of the low-delay complex-value filter banks of the present invention instead of the conventional QMF filter banks makes it possible to significantly reduce the overall computational delay to a value of only 31.3 ms.

[0255] To assess the quality of the filter banks of the present invention and systems comprising one or more filter banks, auditory tests have been carried out from which it can be concluded that the filter banks of the present invention allow maintaining the quality level provided by the AAC-LD codec and do not cause any signal degradation, both in the SBR mode using complex values ​​and in the low power SBR mode using real values. Thus, the delay-optimized filter banks of the present invention do not introduce any decrease in sound quality, while providing the ability to reduce delays by more than 10 ms. In the case of transient elements, you can even observe a slight but statistically insignificant improvement. The above improvement was observed when listening to the sounds of castanets and bells.

[0256] In order to further check whether the downsampling process of the 32-band filter bank of the present invention works equally well when using the filter banks of the present invention and QMF filter banks, the following tests were carried out. First, the log-sine signal was analyzed using a down-sampled 32-band filter bank, with the top 32 bands initialized by zero values ​​added. The result was then synthesized using a 64-band filter bank, downsampled again and compared with the original signal. A signal / noise ratio (SNR) of 59.5 dB was obtained when using a conventional QMF prototype filter. However, when using the filter bank of the present invention, a signal / noise ratio (SNR) of 78.5 dB was obtained, which means that the filter banks of the present invention also operate in a downsampled version with a quality at least comparable to the original QMF filter banks.

[0257] To demonstrate that the delay-optimized unsymmetrical filter bank used in the embodiments of the present invention does not introduce additional values ​​compared to a classic filter bank including a symmetrical prototype, asymmetrical prototypes and symmetrical prototypes showing the same delays are compared below.

[0258] Fig. 15a shows a comparison of the far frequency response of a filter bank according to the present invention comprising a low delay window (graph 800) with the frequency response of a filter bank using a sine function of 128 samples (graph 810). Fig. 15b shows an enlargement of the near frequency response of the same filter banks having the same window functions as in Fig. 15a.

[0259] Direct comparison of the graphs 800, 810 indicates that the frequency response of the filter bank using the low delay filter bank according to the present invention is significantly better than the corresponding frequency response of the filter bank using the sine function with a length of 128 samples and the same delay.

[0260] Also, Figure 16a compares various window functions with a total delay of 127 samples. The 64-band CLDFB filter bank has a total delay of 127 samples, which includes framing delay and overlay delay. A modulated filter bank with a symmetrical prototype and with the same delay therefore has a prototype with a length of 128 samples, as already illustrated with reference to Figs. 15a and 15b. For these 50% overlap filter banks, modified discrete cosine transform (MDCT), sine functions or Kaiser-Bessel windows generally provide a sufficient selection of prototypes. Fig. 16a is therefore a review comparison of the frequency response of a filter bank including a low delay window such as the prototype of the present invention with the frequency responses of alternative symmetrical prototypes with the same delay. In addition to the frequency response of the filter bank according to the present invention (diagram 800) and the frequency response of the filter bank using the sine function (diagram 810), as already shown in Fig. 15a and Fig. 15b, two KBD windows based on α parameters are also visible here = 4 (chart 820) and α = 6 (chart 830). In Fig. 16a and the enlargement of Fig. 16a in Fig. 16b it is clearly seen that by using the filter bank of the present invention comprising an asymmetrical window function or a prototype filter function with the same delay it is possible to obtain a much better frequency response.

[0261] To demonstrate this advantage in a more general case, Fig. 17 shows two prototype filter banks with delay values ​​different from the delay values ​​of the filter banks described above. The filter bank of the present invention shown in Fig. 15 and Fig. 16 has an overall delay of 127 samples, which corresponds to an overlap of 8 blocks in the past and 0 blocks in the future (CLDFB 80), while in Fig. 17 presents for comparison the frequency responses of two different filter bank prototypes having the same delay of 383 samples. More specifically, Fig. 17 shows the frequency response of an unsymmetrical prototype filter bank (chart 840) according to the present invention, which is based on the imposition of 6 blocks of time-domain samples in the past and 2 blocks of time-domain samples in the future (CLDFB 62). In fig. 17 the frequency response (diagram 850) of the corresponding symmetrical prototype filter function is also shown, which also has a delay of 383 samples. It can be seen that with the same delay value, the asymmetrical prototype or window function allows for a better frequency response than is the case with the symmetrical window function or prototype filter. This illustrates the possibility of a better compromise between delay and quality, as outlined earlier in the description.

[0262] Fig. 18 shows the phenomenon of temporal masking of human hearing. If the sound or tone occurs at the time indicated in line 18 by line 860, the masking phenomenon regarding tone or sound frequency and neighboring frequencies occurs about 20 ms before the start of the current sound. This phenomenon is called initial masking and is one of the psychoacoustic properties of human hearing.

[0263] In the situation shown in Fig. 18, the sound remains audible for about 200 ms, up to the point marked by line 870. At this time, the human hearing masker is active, which is also called parallel masking. After the end of the sound (indicated by line 870), frequency masking at adjacent tone frequencies slowly disappears in about 150 ms, as shown in Figure 18. This psychoacoustic phenomenon is also called end masking.

[0264] Fig. 19 shows a comparison of the forward echo of a conventional signal encoded using the HE-AAC codec and a signal encoded using the HE-AAC codec based on a filter bank including a low delay filter bank (CMLDFB) according to the present invention. Fig. 19a shows the original castanet time signal that has been processed by a system including enhanced high efficiency audio codec (HEAAC). The output of the system based on the conventional HE-AAC codec is shown in Figure 19b. A direct comparison of the two signals, the original time signal and the HE-AAC codec output indicates that there is a noticeable pre-echo before the castanets sound in the area marked by arrow 880 in the HE-AAC codec output.

[0265] Fig. 19c shows an output of a system including a HE-AAC codec based on filter banks including the CMLDFB windows of the present invention. The same original time signals as shown in Fig. 19a processed using the filter banks of the present invention show a significant reduction in the pre-echo before the start of the castanets signal, which is indicated in arrow 19c by arrow 890. Due to the pre-masking phenomenon described with reference to Fig. 18, the overtaking echo phenomenon indicated in Fig. 19c by arrow 890 is masked much better than the overlapping echo phenomenon indicated by arrow 880 which occurs with the conventional HEAAC codec. The leading echo effect of the filter banks of the present invention, which is also the result of a significant reduction in delay compared to conventional filter banks, results in a much better signal adapted to the time masking properties and psychoacoustic characteristics of human hearing. As a result, as already noted for listening tests, the use of filter banks according to the present invention can even lead to an increase in sound quality, which is the result of reduced delay.

[0266] Embodiments of the present invention do not increase the computational complexity compared to conventional filter banks. Low-delay filter banks use the same filter length and modulation mode as, for example, QMF filter banks for SBR systems, so there is no increase in computational complexity. Regarding the memory requirements, due to the asymmetrical nature of the prototype filters, the requirements for the ROM (read-only memory) used by the synthesis filter bank increase by about 320 words in the case of a filter bank based on N = 64 samples per block and T = 10 blocks per frame. For the SBR system, memory requirements increase by a further 320 words if the analysis filter is stored separately.

[0267] The current ROM requirements for the AACELD core are about 2.5 thousand words, and for SBR implementation an additional 2.5 thousand words, the ROM requirements increase moderately by about 10%. If low memory requirements are the most important, there is the possibility of developing a compromise between memory requirements and computational complexity by using linear interpolation to generate an analysis filter based on a synthesis filter, as shown with reference to Fig. 3 and equation (15). This interpolation operation increases the number of instructions executed by about 3.6%. Replacing conventional QMF filter banks in the SBR module design with the low delay filter banks of the present invention thus allows reducing the delay in some embodiments of the invention by more than 10 ms without degrading sound quality or increasing computational complexity.

[0268] Embodiments of the present invention therefore relate to an analysis or synthesis window or window device or method. Also described is an analysis or synthesis filter bank or a method for analyzing or synthesizing a signal using a window. Of course, a computer program comprising one of the above methods is also disclosed.

[0269] Implementation of embodiments of the present invention may be carried out in a hardware, software, or combination of the above. Data, vectors and variables generated, received or otherwise stored for processing may be stored in various types of memory, such as random access memory, buffers, read only memory, non-volatile memory (e.g. EEPROM or flash memory) ) or other media such as magnetic or optical memories. The location in memory can be, for example, in the form of one or more memory modules enabling the storage or storage of an appropriate amount of data such as variables, parameters, vectors, matrices, window coefficients or other data or information.

[0270] Software implementations may be implemented on a variety of computers, computer-like systems, integrated circuits designed to perform a specific function (ASIC), or other integrated circuits.

[0271] Depending on the specific requirements associated with implementing the methods of the invention, embodiments of the methods of the present invention may be implemented in hardware or in software, or in the form of a combination of the above solutions. The implementation may be in the form of a digital data carrier, in particular a DVD or CD disc or other disk on which control signals are readable with the use of electronic devices cooperating with a programmable computer system which enables carrying out the methods according to the present invention. The present invention is thus generally in the form of a computer program saved on a medium that can be machine readable, wherein the program code enables, after running it by means of a computer, processor or integrated circuit, to carry out the methods according to the present invention. In other words, the embodiments of the present invention are therefore in the form of a computer program containing program code that, when run by means of a computer, enables the implementation of at least one of the methods of the invention.

[0272] The apparatus for generating the audio subband values ​​in the audio subband channels according to some embodiments of the present invention includes an analysis window module (110) that allows windowing of the frame (120) of input audio signal samples in the time domain in a time order from the previous sample to a later sample using the window analysis function (190) comprising the first group (200) of window coefficients including the first part of the window coefficient sequence and the second group (210) of the window coefficients comprising the second part of the window coefficient sequence, the first part comprising a smaller number of window coefficients than the second part, the energy value of the window coefficients contained in the first part is greater than the energy value of the window coefficients contained in the second part, the first group of window coefficients is used to window the last samples in the time domain, while the second group of window coefficients is used to window earlier samples in the time domain, and the calculator (170) enabling the calculation of the subband range of the audio signal using the windowed samples.

[0273] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the analysis window function (190) is asymmetrical with respect to the window coefficient sequence.

[0274] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that the energy value of the window coefficients contained in the first part is equal to or greater than 2 / 3 energy values ​​of all window coefficients of the window coefficient sequence, and the energy value of the window coefficients contained in the second part of the window coefficients is less than or equal to 1/3 of the energy value of all window coefficients of the window coefficient sequence.

[0275] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that the first portion of the window coefficients comprises 1/3 or less than 1 / 3 total number of window coefficients of the window coefficient sequence, and the second part comprises 2/3 or more than 2/3 of the total number of window coefficients of the window coefficient sequence.

[0276] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that the midpoint of the window coefficients of the window analysis function (190) corresponds to the actual value in index range of the first part of the window coefficients.

[0277] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the analysis window function (190) is strictly monotonically decreasing from the window ratio having the largest absolute value of all window coefficients of the analysis window function (190) to the window ratio of the window coefficient sequence used to window the last audio signal in the time domain.

[0278] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window (110) is configured such that the analysis window (190) has an oscillating character.

[0279] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the window coefficient corresponding to the index n = (T-1) N has an absolute value in the range of 0.9 to 1.1, where the index of the sequence of window coefficients is an integer from 0 to N · T-1, the window coefficient used to window the last input audio signal sample in the time domain of the frame (120) is the coefficient corresponding to the index N - T - 1, the analysis window module (110) is configured in such a way, that the frame (120) of the time domain audio input samples includes a sequence of T blocks (130) of the time domain audio input samples arranged from the earliest to last input time domain audio samples from the frame (120), each block includes N input time domain audio samples, and T and N are positive integers, where T is greater than 9.

[0280] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that the window coefficient corresponding to the index n - N · T - 1 has a value absolute less than 0.02.

[0281] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window (110) is configured in such a way that the windowing includes multiplication of input samples of the audio signal in the x (n) time domain of the frame (120) to obtain windowed samples from (n) a windowed frame based on an equation

<img file="PL1994530T3_D0024.tif" />

where n is an integer indicating the index of the sequence of window coefficients from 0 to N · T - 1, c (n) is the window coefficient of the analysis window function corresponding to the index n, x (N T-1) is the last input signal sample time-domain audio of the frame (120) of time-domain input audio samples, the analysis window (110) is configured in such a way that the frame (120) of the time domain audio input samples includes a sequence of T blocks (130) of the time domain audio input samples arranged from the earliest to last input time domain audio samples from the frame (120), each block includes N input time domain audio samples, and T and N are positive integers, where T is greater than 4.

[0282] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the window coefficients c (n) meet the relationships given in the table in Attachment

4.

[0283] In the apparatus for generating the audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the device (100) is configured to use inverted analysis window function (190) or have reverse indexes of the synthesis window function (370) used to process the subband values ​​of the audio signal.

[0284] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the first part of the analysis window function includes a window factor having a maximum value greater than 1.

[0285] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that all window coefficients of the window coefficient sequence are window coefficients of real values.

[0286] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the frame (120) of the time-domain input audio samples includes a sequence of T blocks (130) of the time-domain input audio samples arranged from the earliest to last input of the time-domain audio signal from the frame (120), each block includes N input time domain audio samples, and T and N are positive integers, where T is greater than 4.

[0287] In an apparatus for generating audio subband values ​​in audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the window includes element-dependent multiplication of input audio signal samples in the art. frame time (120) by the window coefficients of the window coefficient sequence.

[0288] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that each input audio signal sample in the time domain is dependent from the element multiplied by the window coefficient of the analysis window function, according to the time domain input signal sequence and the window coefficient sequence.

[0289] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that for each input audio signal in the time domain from the frame ( 120) input time-domain audio signal samples exactly one windowed sample is generated.

[0290] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that the window coefficient corresponding to the index of the coefficient n = (T-3) . N has a value less than -0.1, where the index of the window coefficients sequence is an integer from 0 to NT - 1, and the window coefficient used to window the last input sample of the audio signal in the time domain is the coefficient corresponding to the N · index T - 1.

[0291] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that the first portion of the window coefficients comprises 3/2 · N window coefficients, and the second part of the window coefficients includes (T-3/2) · N window coefficients of the window coefficient sequence.

[0292] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the window coefficients c (n) meet the relationships given in the table in Attachment

3.

[0293] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured in such a way that the window coefficients c (n) meet the relationships given in the table in Attachment

2.

[0294] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the analysis window module (110) is configured such that window coefficients c (n) meet the relationships given in the table in Attachment

1.

[0295] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the device (100) is configured in such a way that the current frame (120) containing the processing time input signal samples to be processed is generated by shifting (T-1) the last blocks of the immediately preceding time frame (120) of input time signal audio samples one block towards the earlier input signal samples time domain audio and the addition of one block (220) of new time domain audio samples in the form of a block containing the last audio samples in time domain of the current frame (120).

[0296] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the device (100) is configured in such a way that the current frame (120) containing the processing time input signal samples in the time domain x (n) to be processed is generated by shifting the input time signal audio samples in the time domain xprev (n) directly prior frame (120) the input time signal audio samples in the time domain w based on the equation

<img file="PL1994530T3_D0025.tif" />

for a time or sample index n = 32, 319, and the analysis window module (110) further allows generating time-domain audio signal samples x (n) of the current frame (120) time-domain audio signal samples by inputting 32 consecutive received time-domain audio signal samples in order of decreasing time index or time domain audio signal samples for time domain x (n) audio signal samples of the current frame (120) starting from the time index or sample n = 31.

[0297] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the calculator (170) includes a time / frequency converter enabling the generation of audio subband values ​​in such a way that all subband values ​​based on the frame (150) of windowed samples is a spectral representation of the windowed samples of the frame (150) of windowed samples.

[0298] In an apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the time / frequency converter allows the generation of complex audio or real values ​​audio band subband values.

[0299] In an apparatus for generating audio subband values ​​in an audio subband channels according to some embodiments of the present invention, the calculator (170) allows one audio subband value to be calculated for each input audio signal sample in the time domain of one input block (130) time domain audio samples, wherein the calculation of each audio subband value for each input time-domain audio signal sample of one block (130) of the time-domain audio input samples is based on windowed samples of the windowed frame (150).

[0300] In an apparatus for generating audio subband values ​​in audio subband channels according to some embodiments of the present invention, the calculator (170) allows calculating the audio subband values ​​based on multiplication of windowed samples (150) by the harmonic oscillation function for each value band sub-range and summation of multiplied windowed samples, where the frequency of the harmonic oscillation function is based on the central frequency of the relevant sub-band values ​​of the sub-band values.

[0301] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the calculator (170) is configured in such a way that the harmonic oscillation function is in the form of an exponential function with complex values, a sine function or a cosine function .

[0302] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the calculator (170) allows calculating the audio subband range values ​​wk1 based on the equation = Σ ^Ζ(^{Π +} 7 * ⁶⁴) for n = 0, ..., 63 and «u = Σ ^at« ·² · N-0

- (^ + 0-5) - (2n - 95) 1 for k = 0, 31, where z (n) is a windowed sample corresponding to the index n, k is the index of the subband range, 1 is the block index (180) values ​​of the subband ranges audio signal, while fosc (x) is an oscillating function depending on the variable x with real values.

[0302] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the calculator (170) is configured such that the oscillatory function fosc (x) has the form

AcW = exp (i * x) or * □ «(*) = cos (x) or = sin (x) where it is an imaginary unit.

[0304] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the device (100) enables processing of the frame (120) of real-time time domain input audio samples.

[0305] In the apparatus for generating audio subband values ​​in the audio subband channels according to some embodiments of the present invention, the device (100) allows providing a signal indicating a synthesis window function (370) which should be used to process the signal subband values audio or indicating an analysis window function (190) that was used to generate the subband values ​​of the audio signal.

[0306] The apparatus for generating time-domain audio signal samples according to some embodiments of the present invention includes a calculator (310) for calculating the sequence (330) of intermediate time-domain samples based on audio subband values ​​in the audio subband channels, wherein the sequence includes earlier time domain intermediate audio samples and later time domain intermediate audio samples, a synthesis window module (360) that allows windowing of a sequence (330) of intermediate time-domain samples using the synthesis window function (370) including a window coefficient sequence to obtain windowed intermediate time-domain samples, wherein the synthesis window (370) comprises a first group (420) of window coefficients comprising the first part of the window coefficient sequence and a second group (430) of window coefficients comprising the second part of the window coefficient sequence, the first part having a smaller number of window coefficients than the second group, the energy value of the window coefficients in the first part is greater than the energy value of the window coefficients in the second part, the first group of window coefficients is used to window later intermediate time domain samples, while the second group of window coefficients is used to window earlier intermediate time domain samples, and the output stage performing the application with addition (400) for processing intermediate samples in the field time to obtain time domain samples.

[0307] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the energy value of the window coefficients contained in the first part of the window coefficients is greater than or equal to 2/3 of the energy value all coefficients of the window of the synthesis window (370), and the energy value of the second part of the window coefficients is less than or equal to 1/3 of the energy value of all the window coefficients of the synthesis window function.

[0308] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the first portion of the window coefficients comprises 1/3 or less than 1/3 of the total number of sequence window coefficients window coefficients, and the second part comprises 2/3 or more than 2/3 of the total number of window coefficients of the window coefficient sequence.

[0309] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured in such a way that the midpoint of the window coefficients of the synthesis window function (370) corresponds to the actual value in the index range of the first part window coefficients.

[0310] In an apparatus for generating time-domain audio signal according to some embodiments of the present invention, the synthesis window (360) is configured in such a way that the synthesis window function is strictly monotonically increasing from the window coefficient of the window coefficient sequence sequence used to window the last intermediate sample of the audio signal in the time domain to the window coefficient having the largest absolute value of all the window coefficients of the synthesis window function.

[0311] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the synthesis window function (370) has an oscillating character.

[0312] In the time domain audio signal generating apparatus according to some embodiments of the present invention, a window coefficient corresponding to the index n = N has an absolute value in the range from 0.9 to 1.1, wherein the window coefficient sequence index is a number integer from 0 to T · N - 1, the window coefficient used to window the last intermediate time domain sample is the coefficient corresponding to the index n = 0, where T is an integer greater than 4, indicating the number of blocks contained in the frame (330) of intermediate time domain samples, and the device (300) generates a block (410) of time domain audio samples including N time domain audio samples where N is a positive integer.

[0313] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured in such a way that the window coefficient corresponding to the index n = 0 has an absolute value less than or equal to 0.02.

[0314] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the window coefficient corresponding to the index n = 3N is less than -0.1 and the device (300 ) allows block (410) time domain audio samples to be generated comprising N time domain audio samples where N is a positive integer. In the time domain audio signal generating apparatus of the present invention, the synthesis window module (360) is configured such that the window winding comprises the multiplication of the time domain audio signal samples g (n) the sequence of the time domain audio signal samples to obtaining windowed samples from (n) a windowed frame (380), based on the equation ζ (η) = g (n) c (T. W - 1 - λ) for n = 0, T · N - 1.

[0315] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the window coefficients c (n) meet the relationships given in the table in Annex 4.

[0316] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the apparatus (300) is configured to use the synthesis window function (370) in inverted form or having inverse indexes of the window function of analysis (190) ) used to generate the subband value of the audio signal.

[0317] In an apparatus for generating time domain audio samples according to some embodiments of the present invention, the device (300) allows generating a block (410) of time domain audio samples, wherein the block (410) time domain audio samples comprises N samples time domain audio signal where N is a positive integer.

[0318] In an apparatus for generating time-domain audio signal according to some embodiments of the present invention, the device (300) allows generating a block (410) of time-domain audio signal samples based on a block (320) of audio subband range values ​​including N subrange values audio signal bands, and the calculator (310) calculates the sequence (330) of time domain intermediate audio samples comprising T · N time domain intermediate audio samples, where N is a positive integer.

[0319] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured in such a way that the synthesis window function is unbalanced relative to the window coefficient sequence.

[0320] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the first part includes the maximum value of all window coefficients of the synthesis window function having an absolute value greater than 1.

[0321] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the first portion includes 3/2 · N window coefficients and the second portion of window coefficients includes (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.

[0322] In an apparatus for generating time-domain audio signal samples according to some embodiments of the present invention, the synthesis window (360) is configured in such a way that the windowing of the sequence of intermediate time-domain samples includes an element-dependent multiplication of intermediate time-domain samples by window coefficients.

[0323] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that each intermediate time domain sample is multiplied by the factor of the window synthesis window function (370), according to the sequence of intermediate time-domain samples and the sequence of window coefficients.

[0324] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window module (360) is configured such that the window coefficients of the synthesis window function (370) have actual values.

[0325] In the time domain audio signal generating apparatus of the present invention, the synthesis window (360) is configured such that the window coefficients c (n) meet the relationships given in the table in Annex 3.

[0326] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the synthesis window (360) is configured in such a way that the window coefficients c (n) meet the relationships given in the table in Annex 2.

[0327] In the time domain audio signal generating apparatus of the present invention, the synthesis window (360) is configured such that the window coefficients c (n) meet the relationships given in the table in Annex 1.

[0328] In an apparatus for generating time-domain audio signal samples according to some embodiments of the present invention, the calculator (310) allows the calculation of intermediate time-domain samples of the sequence of intermediate time-domain samples based on the multiplication of audio subband values ​​by harmonic vibration function and summation multiplied subband values ​​of the audio signal, where the frequency of the harmonic oscillation function is based on the center frequency of the respective subband.

[0329] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the calculator (310) is configured in such a way that the harmonic oscillation function is an exponential function with complex values, a sine function or a cosine function.

[0330] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the calculator (310) enables the calculation of real time intermediate real time samples based on subband values ​​of complex audio or real values.

[0331] In an apparatus for generating time-domain audio signal samples according to some embodiments of the present invention, the calculator (310) allows calculating the sequence of intermediate time-domain samples with real values ​​of (i, n) based on the equation

<img file="PL1994530T3_D0026.tif" />

for integers n in the range from 0 to N · T - 1, where Re (x) is the real part of the complex number x, n = 3.14 ... is an automorphic number, and fosc (x) is a function ą harmonic vibrations, where

<img file="PL1994530T3_D0027.tif" />

when the subband values ​​of the audio signal input into the calculator are complex values, with the imaginary unit, and where

<img file="PL1994530T3_D0028.tif" />

when the subband values ​​of the audio signal input into the calculator (310) are real values.

[0332] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the calculator (310) includes a time / frequency converter allowing the generation of intermediate sequences of time domain samples in such a way that all subband values ​​entered into the calculator (310) ) are a spectral representation of time sequence intermediate samples.

[0333] In an apparatus for generating time-domain audio signal samples according to some embodiments of the present invention, the time / frequency converter enables the generation of intermediate time-domain sample sequences based on subband values ​​of complex or real values ​​audio signal.

[0334] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the calculator (310) calculates the intermediate sequence of time domain samples g (n) based on the subband values ​​of the audio signal X (k) by means of the equation

<img file="PL1994530T3_D0029.tif" />

for integers n in the range of 20N - 1 to 2N,

<img file="PL1994530T3_D0030.tif" />

for integers n in the range 0 to 2N - 1 and y (2N j + Jej = v (4Wj + Je) y (2N j + W + Je) = v (4Nj + 3N + Je) for integers j in the range of 0 to 4 and integers k in the range of 0 to N - 1, where N is an integer indicating the number of values ​​of the audio subband and the number of samples of the audio signal in the time domain, v is a vector with real values . vprev is a vector with real values ​​of directly generated time domain audio samples, and is an imaginary unit, and π is an automorphic number.

[0335] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the calculator (310) calculates the intermediate sequence of time domain samples g (n) based on the subband values ​​of the audio signal X (k) by means of the equation ^v(ⁿ) = Σ

Jt = .O ^V(«) = For integers n in the range from 20N - 1 to 2N, • π ^somethingthese &lt;*⁺'⁽²ⁿ ~⁽ⁱⁿ ’^1})) for integers n in the range from 0 to 2N - 1 and g (2N · j + ή * v (4Wj + Jt) g (2N · j + N + k) = v (4Nj + 3N + k) for integers j in the range of 0 to 4 and integers k in the range of 0 to N - 1, where N is an integer indicating the number of subband values ​​of the audio signal and the number of audio signal samples in the time domain, v is a vector about real values, vprev is a vector with real values ​​of directly generated time domain audio samples, and is an imaginary unit, and π is an automorphic number.

[0336] In an apparatus for generating time-domain audio signal according to some embodiments of the present invention, the add-on output stage (400) enables processing of windowed intermediate time-domain samples by overlay, based on T successively delivered blocks (320) of value audio signal subbands.

[0337] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the overlay output step (400) allows providing time domain samples out1 (n), where n is an integer indicating the sample index based on equation

Γ-1 outjfn) = ^from(i-fr), n + t N is where zi, n is a windowed intermediate time domain sample corresponding to the sample index n and frame index 1 of the frame or sequence from 0 to T - 1, and 1 = 0 corresponds to the last frame or sequences and smaller values ​​of 1 previously generated frames or sequences.

[0338] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the overlay output step (400) allows providing time domain samples out1 (k) based on the equation out (k) = yi w (N · N + k) jr-o where w is a vector including windowed intermediate samples in the time domain, and k is an integer indicating an index in the range from 0 to (N-1), [0339] In the time domain audio signal generating apparatus according to some embodiments of the present invention, the device (300) allows receiving a signal indicating an analysis window function (190) that has been used to generate a subband value of an audio signal or indicating a synthesis window function (370) ), which should be used to process the subband value of the audio signal.

[0340] In some embodiments of the present invention, the encoder (510) includes a device (560) for generating audio subband values ​​in the audio subband channels of the present invention.

[0341] In some embodiments of the present invention, the encoder (510) further includes a quantization and coding module (570) coupled to the device (560) for generating audio subband values, enabling the quantization and coding of audio subband values ​​provided at the output of the device ( 560) and provides the output with quantized encoded subband values ​​of the audio signal.

[0342] In some embodiments of the present invention, the decoder (580) includes a device (600) for generating time domain audio signal samples according to the present invention.

[0343] In some embodiments of the present invention, the decoder (580) further includes a decoding and dequantizing module (590) enabling receiving quantized encoded values ​​of the audio subband ranges, connected to a device (600) for generating time domain audio samples and enabling transmission to devices (600) of quantized encoded audio subband values ​​in the form of audio subband values.

[0344] In some embodiments of the present invention, the SBR encoder (520) includes a device (530) for generating audio subband values ​​based on a frame of input time domain audio samples input into the SBR encoder (520) and an SBR separating module (540) ) connected to the device (530) for generating the subband values ​​of the audio signal and enabling the output and sharing of SBR parameters on the basis of the subband values audio signal.

[0345] In some embodiments of the present invention, the system (610) includes a device (620) for generating audio subband values ​​based on a frame of input time domain audio samples input into the system (610) and a device (640) for generating signal samples time domain audio based on the audio subband values ​​generated by the device (640) for generating audio subband values.

[0346] In some embodiments of the present invention, the system (610) is in the form of an SBR decoder.

[0347] In some embodiments of the present invention, the system further includes an HF generator (630) connected between the device (620) for generating audio subband values ​​and the device (640) for generating time domain audio samples, enabling receiving SBR data and modifying and adding audio subband values ​​based on SBR data and audio subband values ​​transmitted from the device (620) to generate audio subband values.

[0348] In all devices and methods of the present invention, depending on the implementation details, in order to obtain window coefficients based on the values ​​given in the tables in Annexes 1 and 3, it is possible to implant additional changes of signs of the window coefficients corresponding to indexes 128 to 255 and 384 to 511 (multiplied by the value (-1)). In other words, the window coefficients of the window function are based on the window coefficients given in the table in Annex 1. To obtain the window coefficients shown in the drawings, the window coefficients given in the table corresponding to indexes 0 to 127, 256 to 383 and 512 to 639 should be multiplied by the value (+1) (no sign change), and the window coefficients corresponding to indexes 128 to 255 and 384 to 511 should be multiplied by the value (-1) (sign change) to get the window coefficients given for the window function. Do the same with the bundles given in the table in Annex 3.

[0349] The apparatus for generating the audio subband values ​​in the audio subband channels according to some embodiments of the present invention includes an analysis window module (110) that allows windowing of the frame (120) of input audio signal samples in the time domain in a time sequence from the earliest samples to the last sample using the window analysis function 190 including the sequence of window coefficients to obtain windowed samples, wherein the window function of analysis includes the first number of window coefficients obtained based on a larger window function including the sequence of a larger second number of window coefficients, window coefficients of the window function are obtained by interpolation of the window coefficients of the larger window function, and the second number is an even number. It also includes a calculator (170) for calculating audio subband values ​​based on windowed samples.

[0350] An embodiment of the present invention in the form of the device 100 may be optionally adapted to interpolate the window coefficients of the larger window function to obtain the window coefficients of the window function.

[0351] Some embodiments of the present invention in the form of the device 100 may be modified such that the configuration of the analysis window module (110) causes the windowing to include multiplication of the input audio signal samples in the time domain x (n) of the frame (120) to obtain windowed samples from a (n) windowed frame based on an equation

<img file="PL1994530T3_D0031.tif" />

where n is an integer indicating the index of the sequence of window coefficients from 0 to N · T - 1, c (n) is the window coefficient of the analysis window function corresponding to the index n, x (N T-1) is the last input sample of the audio signal in the field time frame (120) of input audio signal samples in time domain, the analysis window (110) is configured in such a way that the frame (120) of the time domain audio input samples includes a sequence of T blocks (130) of the time domain audio input samples spaced from the earliest to last input time domain audio samples from the frame (120), each block includes N input samples time domain audio signal, and T and N are positive integers, where T is greater than 4.

[0352] Some embodiments of the present invention in the form of the device 100 may be modified in such a way that the analysis window function 190 includes a first group of window coefficients 200 comprising the first part of the window coefficient sequence and a second group of window coefficients 210 comprising the second part of the window coefficient sequence which first part has fewer window coefficients than the second part, the energy value of the window coefficients contained in the first part is greater than the energy value of the window coefficients contained in the second part, the first group of window coefficients is used to window the last samples in the time domain, and the second group of window coefficients is used to window the earlier samples in the time domain.

[0353] Some embodiments of the present invention in the form of the device 100 may be modified in such a way that the analysis window function (190) is in the form of a time-inverted or having inverse indexes of the synthesis window function (370) used to process the audio subband value.

[0354] The apparatus 300 for generating time-domain audio signal samples according to some embodiments of the present invention includes a calculator 310 enabling the calculation of a sequence of intermediate time-domain samples 330 based on audio subband values ​​in the audio subband channels, the sequence including prior indirect time domain audio samples and subsequent time domain intermediate audio samples, 360 synthesis window module that allows windowing of a sequence of 330 time domain samples using a synthesis window function 370 including a window coefficient sequence to obtain windowed intermediate time domain samples, where the synthesis window function includes the first number of window coefficients obtained based on a larger window function including the sequence of a larger second number of window coefficients, window coefficients of the window function are obtained by interpolation of the window coefficients of the larger window function, and the second number is an even number. It also includes an initial stage performing an application with an addition of 400 to process windowed intermediate time domain samples to obtain time domain samples.

[0355] Some embodiments of the present invention in the form of the device 300 may be modified in such a way that interpolation of the window coefficients of the larger window function is used to obtain the window coefficients of the window function.

[0356] Some embodiments of the present invention in the form of the device 300 can be modified in such a way that the synthesis window module (360) is configured in such a way that the windowing involves the multiplication of intermediate audio signal samples in the time domain g (n) of the intermediate sample sequence in time domain to obtain windowed samples from the (n) windowed frame 380 based on the equation

<img file="PL1994530T3_D0032.tif" />

for n = 0,., T · N - 1.

[0357] Some embodiments of the present invention in the form of the device 300 may be modified in such a way that the synthesis window module (360) is configured in such a way that the synthesis window function 370 includes a first group of window coefficients 420 comprising the first part of the window coefficient sequence and a second group of 430 window coefficients comprising the second part of the window coefficient sequence, wherein the first part contains a smaller number of window coefficients than the second group, the energy value of the window coefficients in the first part is greater than the energy value of the window coefficients in the second part, the first group of window coefficients is used for windowing later intermediate time domain samples, and the second group of coefficients windows are used to window earlier intermediate time domain samples.

[0358] Some embodiments of the present invention in the form of the device 300 may be modified in such a way that the synthesis window function 370 is inverted in the form of or has inverse indexes the window function of the analysis 190 used to generate the subband values ​​of the audio signal.

[0359] It should be noted that the concept of the present invention may use equations to introduce additional delays, factors, additional factors, and other simple functions. It is also possible to include simple constant, fixed sum components and so on. Algebraic transformations, equivalent transformations and approximations (e.g., Taylor approximation) that do not change the results of the equations in a significant way or do not change them at all are also included in the invention. In other words, both minor modifications and transformations leading to the same result are included in the invention if the equations or expressions are based on the disclosed equations or expressions.

[0360] Although the invention has been described and presented with reference to its specific embodiments, those skilled in the art are aware of the fact that various changes in form and detail can be made without departing from the scope of the invention. It will be appreciated that various changes may be made to adapt the invention to other embodiments without departing from the broad concept of the invention which is set forth herein and disclosed in the appended claims.

Annex 1 [0361] in [0] = 1.129580193872797e-002 in [1] = 2.353059744904218e-002 in [2] = 3.450718748721251e-002 in [3] = 4.634695977000525e-002 in [4] = 5.918677345174197e-002 in [5] = 7.325978412117062e-002 in [6] = 8.829745229234007e-002 in [7] = 1.042033024802571e-001 in [8] = 1.206924277410051e-001 in [9] = 1.376149808913910e-001 in [10] = 1.547461142258783e-001 in [11] = 1.719726384566089e-001 in [12] = 1.891590407342011e-001 in [13] = 2.062605107774960e-001 in [14] = 2,232276864673650e-001 in [15] = 2,400768261284114e-001 in [16] = 2.568176309566753e-001 in [17] = 2.734977190313227e-001 in [18] = 2.901491317310591e-001 in [19] = 3.068186515423912e-001 in [20] = 3.235298682841570e-001 in [21] = 3.403074146062977e-001 in [22] = 3.571527896130669e-001 in [23] = 3.740643974275026e-001 in [35] = 5.764734796907189e-001 in [36] = 5.930981800982896e-001 in [37] = 6.096690552916387e-001 in [38] = 6.261725236758639e-001 in [39] = 6.425939632009995e-001 in [40] = 6.589148753746076e-001 in [41] = 6,751199626157149e-001 in [42] = 6.911981575264606e-001 in [43] = 7.071447728928043e-001 in [44] = 7.2229599104052475e-001 in [45] = 7.386515025302785e-001 in [46] = 7.542294504292890e-001 in [47] = 7.697093346240386e-001 in [48] = 7.851012620144958e-001 in [49] = 8.004165237845137e-001 in [50] = 8.156523162880560e-001 in [51] = 8.308039608112368e-001 in [52] = 8,458450064727010e-001 in [53] = 8.607492455327098e-001 in [54] = 8.754640719350776e-001 in [55] = 8.899474405744183e-001 in [56] = 9.04128613801-7367e-001 in [57] ] = 9,179666107725365e-001 in [58] = 9,313874086278087e-001 in [59] = 9,443802853939540e-001 in [60] = 9,568885413848645e-001

<td>in [24] = 3.910243970160607e-001</td><td>in [61] =</td>

<td>in [25] = 4.080154903861317e-001</td><td>in [62] =</td>

<td>in [26] = 4.250144186334534e-001</td><td>in [63] =</td>

<td>in [27] = 4.420013942269341e-001</td><td>in [64] =</td>

<td>in [28] = 4.589582896478246e-001</td><td>in [65] =</td>

<td>in [29] = 4.7587537,45532750e-001</td><td>in [66] =</td>

<td>in [30] = 4.927463828072591e-001</td><td>in [67] =</td>

<td>in [31] = 5.095720854151864e-001</td><td>in [68] =</td>

<td>in [32] = 5.263554446856779e-001</td><td>in [69] =</td>

<td>in [33] = 5.430990601899994e-001</td><td>in [70] =</td>

<td>in [34] = 5.598052330689253e-001</td><td>in [71] =</td>

<td>in [72] = 1.035694432087486e + 000</td><td>and [110]</td>

<td>in [73] = 1.037683165297586e + 000</td><td>and [111]</td>

<td>in [74] = 1.039227995800217e + 000</td><td>and [112]</td>

<td>in [75] = 1.040349586463588e + 000</td><td>and [113]</td>

<td>in [76] = 1.041086497214721e + 000</td><td>and [114]</td>

<td>in [77] = 1.041443375950143e + 000</td><td>and [115]</td>

<td>in [78] = 1.04143.4355650865e + 000</td><td>and [116]</td>

<td>in [79] = 1.09109.3189216171e + 000</td><td>and [117]</td>

<td>in [80] = 1.040262316588456e + 000</td><td>and [118]</td>

<td>in [81] = 1.039061496136853e + 000</td><td>and [119]</td>

<td>in [82] = 1.037422300157921e + 000</td><td>and [120]</td>

<td>in [83] = 1.035311720204252e + 000</td><td>and [121]</td>

<td>in [84] = 1.032712952177121e + 000</td><td>and [122]</td>

<td>in [85] = 1.029600494883906e + 000</td><td>and [123]</td>

<td>in [86] = 1.025966756910904e + 000</td><td>and [124]</td>

<td>in [87] = 1.021798805583990e + 000</td><td>and [125]</td>

<td>in [88] = 1.017100128250049e + 000</td><td>and [126]</td>

<td>in [89] = 1.011867706519706e + 000</td><td>and [127]</td>

<td>in [90] = 1.006109248754940e + 000</td><td>and [128]</td>

<td>in [91] = 9.998285752401580e-001</td><td>and [129]</td>

<td>in [92] = 9.930379854679836e-001</td><td>and [130]</td>

<td>in [93] = 9.857387823493258e-001</td><td>and [131]</td>

<td>in [94] = 9.779405164766706e-001</td><td>and [132]</td>

<td>in [95] = 9.696426101291272e-001</td><td>and [133]</td>

9,690016637782843e-001

9,807691702375303e-001

9,927543720639498e-001

1,001463112557766e +000

1,006893331637123e +000

1,012508393574432e +000

1,017729040219375e +000

1,022470190536100e +000

1,026615653698808e +000

1,030198648769593e +000

1.03320585058.0933e + 000 = 7.9.08995350037713e-001 = 7.760385598209244e-001 = 7.609051036128973e-001 = 7.45111681431031e-001 = 7.298745530879272e-001 = 7.1148 8872949399959-001 = 6.14 001 = 6.816667882498023e-001 = 6.652304141388827e-001 = 6.486437667370537e-001 = 6.319284031798550e-001 = 6.151031151692835e-001 = 5.981877665956570e-001 = 5.811992722116215e-001 = 5.811992722116215e-001 = 5.811992722116215e-001 = 5.810 5,470652177576862e-001 = 5,299509559653194e-001 = 5,128557121424191e-001 = -4,956175421414453e-001 = -4.782650346610896e-001 = -4.609828932783459e-001 = -4.437530233023859e-001 = -4.265950246465440e-001 = -4.095160467543179e-001

<td>in [96] = 9.608519516143015e-001</td><td>and [134]</td>

<td>in [97] = 9.515674613550604e-001</td><td>and [135]</td>

<td>in [98] = 9.417975696327747e-001</td><td>and [136]</td>

<td>in [99] = 9.315442093447622e-001</td><td>and [137]</td>

<td>in [100] = 9,208194746232827e-001</td><td>and [138]</td>

<td>in [101] = 9,096310803629866e-001</td><td>and [139]</td>

<td>in [102] = 8.979959173503500e-001</td><td>and [140]</td>

<td>in [103] = 8.859232320517536e-001</td><td>and [141]</td>

<td>in [104] = 8.734366852542127e-001</td><td>and [142]</td>

<td>in [105] = 8.605542791988831e-001</td><td>and [143]</td>

<td>in [106] = 8.4472987145504696e-001</td><td>and [144]</td>

<td>in [107] = 8.336863467961255e-001</td><td>and [145]</td>

<td>in [108] = 8.197387292306723e-001</td><td>and [146]</td>

<td>in [109] = 8.054701312929008e-001</td><td>and [197]</td>

<td>in [148] = -1.738542127021508e-001</td><td>and [186]</td>

<td>in [149] = -1.600061812296078e-001</td><td>and [187]</td>

<td>in [150] = -1.464389150679625e-001</td><td>and [188]</td>

<td>in [151] = -1.331544923127771e-001</td><td>and [189]</td>

<td>in [152] = -1.201628679722633e-001</td><td>and [190]</td>

<td>in [153] = -1.074630704470568e-001</td><td>and [191]</td>

<td>in [154] = -9.506966959632511e-002</td><td>and [192]</td>

<td>in [155] = -8.298103104739203e-002</td><td>and [193]</td>

<td>in [156] = -7,120356992726613e-002</td><td>and [194]</td>

<td>in [157] = -5.973741829536090e-002</td><td>and [195]</td>

<td>in [158] = -4.859005767016811e-002</td><td>and [196]</td>

<td>in [159] = -3.775928110298274e-002</td><td>and [197]</td>

<td>in [160] = -2.726484300186575e-002</td><td>and [198]</td>

<td>in [161] = -1.711323992709580e-002</td><td>and [199]</td>

<td>in [162] = -7.298197371320593e-003</td><td>and [200]</td>

<td>in [163] = 2.184256929356781e-003</td><td>and [201]</td>

<td>in [164] = 1.132324047372148e-002</td><td>and [202]</td>

<td>in [165] = 2.012236990754980e-002</td><td>and [203]</td>

<td>in [166] = 2.857528272530154e-002</td><td>and [204]</td>

<td>in [167] = 3.666942822678171e-002</td><td>and [205]</td>

<td>in [168] = 4.439683978044157e-002</td><td>and [206]</td>

-3,925409172155113e-001

-3,756821671788237e-001

-3,589626517817934e-001

-3,423942311297658e-001

-3,259993851088293e-001

-3,097861805973821e-001

-2,937724988593393e-001

-2,779637821990255e-001

-2,623749159988041e-001

-2,470098299603623e-001

-2,318815478758375e-001

-2,169925682529340e-001

-2,023548005388463e-001

-1,879711796686855e-001

1,238868653862843e-001

1,251477258491527e-001

1,261262023246478e-001

1,268280540744526e-001

1,272498700590511e-001

1,273590703506806e-001

1,274567595465545e-001

1,275561350483646e-001

1,273648326872248e-001

1,269415772180714e-001

1,262995646340671e-001

1,254605188749804e-001

1,244269583009826e-001

1,232131583108813e-001

1,218183974842866e-001

1,202545652840080e-001

1,185243106889108e-001

1,166399102636992e-001

1,146042249339280e-001

1,124296184976912e-001

1,101215600923314e-001

<td>in [169] = 5,177964768870787e-002</td><td>and [207]</td>

<td>in [170] = 5.881296711410786e-002</td><td>and [208]</td>

<td>in [171] = 6.550209046893848e-002</td><td>and [209]</td>

<td>in [172] = 7.184073822817207e-002</td><td>and [210]</td>

<td>in [173] = 7.783299328224960e-002</td><td>and [211]</td>

<td>in [174] = 8.347150698567406e-002</td><td>and [212]</td>

<td>in [175] = 8.875756217893037e-002</td><td>and [213]</td>

<td>in [176] = 9.368651761350569e-002</td><td>and [214]</td>

<td>in [177] = 9.826251129465624e-002</td><td>and [215]</td>

<td>in [178] = 1.024804711677230e-001</td><td>and [216]</td>

<td>in [179] = 1.063959559357498e-001</td><td>and [217]</td>

<td>in [180] = 1.098551252869576e-001</td><td>and [218]</td>

<td>in [181] = 1.130180022553412e-001</td><td>and [219]</td>

<td>in [182] = 1.158358935177899e-001</td><td>and [220]</td>

<td>in [183] ​​= 1.183233335449968e-001</td><td>and [221]</td>

<td>in [184] = 1.204854506722672e-001</td><td>and [222]</td>

<td>in [185] = 1.223371395269402e-001</td><td>and [223]</td>

<td>in [224] = 5.911363249658311e-002</td><td>and [262]</td>

<td>in [225] = 5.637219228757212e-002</td><td>and [263]</td>

<td>in [226] = 5.368313072045600e-002</td><td>and [264]</td>

<td>in [227] = 5,105620793438655e-002</td><td>and [265]</td>

<td>in [228] = 4.849284995895640e-002</td><td>and [266]</td>

<td>in [229] = 4.599068181839981e-002</td><td>and [267]</td>

<td>in [230] = 4.355568588898841e-002</td><td>and [268]</td>

<td>in [231] = 4.125570251909672e-002</td><td>and [269]</td>

<td>in [232] = 3.907137550527191e-002</td><td>and [270]</td>

<td>in [233] = 3.696342556744636e-002</td><td>and [271]</td>

<td>in [234] = 3.493300140502248e-002</td><td>and [272]</td>

<td>in [235] = 3.298151059524886e-002</td><td>and [273]</td>

<td>in [236] = 3,110861245410919e-002</td><td>and [274]</td>

<td>in [237] = 2.931525594774175e-002</td><td>and [275]</td>

<td>in [238] = 2.760090729801069e-002</td><td>and [276]</td>

<td>in [239] = 2.597956638848436e-002</td><td>and [277]</td>

<td>in [240] = 2.443433592149451e-002</td><td>and [278]</td>

<td>in [241] = 2.296470793543091e-002</td><td>and [279]</td>

1,076972053405737e-001

1,051641975499523e-001

1,025397604985405e-001

9,982957934346254e-002

9,705239536075722e-002

9,421624116597689e-002

9,133590931873967e-002

8,841813387276727e-002

8,547715661443602e-002

8,251962055343706e-002

7,955570759229536e-002

7,657649751612349e-002

7,360559211914287e-002

7,064948295960993e-002

6,771675107480543e-002

6,480448458935215e-002

6,192692754258131e-002

-5,741103163221257e-003

-5,394569608919965e-003

-5,063851046064050e-003

-4,754191853611012e-003

-4,448993249380505e-003

-4,133639756278191e-003

-3,811612348723333e-003

-3,505531318950422e-003

-3,209092846617964e-003

-2-927159436740159e-003

-2,653818578698405e-003

-2,396404013961463e-003

-2,152379960589273e-003

-1,924844672908215e-003

-1,699160580023900e-003

-1,480542563288228e-003

-1,283280633901446e-003

-1,131859661378862e-003 in [242] = 2.156304510969632e-002 in [243] = 2.023524610221679e-002 in [244] = 1.897505817503749e-002 in [245] = 1.778248750467421e-002 in [246] = 1.665187994388476e-002 in [247] = 1.557759513377242e-002 in [248] = 1.956208586604537e-002 in [249] = 1.361072086117313e-002 in [250] = 1.270747042064656e-002 in [251] = 1.1866210743261470e-002 in [252] = 1.106958962776399e-002 in [253] = 1.033126278863177e-002 in [254] = 9.640298325700842e-003 in [255] = 8.996371481700806e-003 in [256] = -8,407748878436545e-003 in [257] = -7,876393114319395e-003 in [258] = -7,380543918629573e-003 in [259] = -6,925141135202262e-003 in [260] = -6,500502521462604e-003 in [261] = -6,109178606718115e-003 in [300] = -2.004822830002534e-004 in [301] = -6,169854804735951e-004 in [302] = -1.061498982103114e-003 in [303] = - 1.594860949611097e-003 in [304] = -2.124647831574725e-003 in [305] = -2.621537051750861e-003 in [306] = -3.064311083207632e-003 in [307] = -3.460362845825662e-003 in [308] = -3.794425324215804e-003 in [309] = -4.091032597247918e-003 in [310] = -4.369553676668050e-003 in [311] = -4.554811297024067e-003 in [312] = -4.663276675479689e-003 in [313] = -4.722567636185647e-003 in [314] = -4.704321497976561e-003 in [280] = -9.730460256556873e-004 in [281] = -7.677634115875747e-004 in [282] = -5.599347984905645e-004 in [283] = - 3,337966579125254e-004 in [284] = -9,099722643476421e-005 in [285] = 1,498231621816041e-004 in [286] = 4.366447012116811e-004 in [287] = 6.307841647560053e-004 in [288] = 6.150316826138937e-004 in [289] = 8,990255827053560e-004 in [290] = 1.232134364570107e-003 in [291] = 1.471167206249042e-003 in [292] = 1.697652664777771e-003 in [293] = 1.985825255428654e-003 in [294] = 2,172866052963961e-003 in [295] = 1.812176023993582e-003 in [296] = 1.344657262814793e-003 in [297] = 9.373975348172919e-004 in [298] = 5.621720998949145e-004 in [299] = 2.048498552413189e-004 in [338] = 6.944123176012471e-004 in [339] = 7.139919634325070e-004 in [340] = 7.154123487609100e-004 in [341] = 7.376101027486600e-004 in [342] = 6.976561203768226e-004 in [343] = 5.721223454434728e-004 in [344] = 2.934875643581191e-009 in [345] = 1.092526149391273e-004 in [346] = 6.415402443848103e-004 in [347] = 1,194730618383423e-003 in [348] = 1,557112059887280e-003 in [349] = 1.891971801393744e-003 in [350] = 2.225524159129023e-003 in [351] = 2.530906981099261e-003 in [352] = 2.719749515067397e-003 in [315] = -4.636227793039124e-003 in [316] = -4.517190210387324e-003 in [317] = -4.351667566540186e-003 in [318] = -4.135130493071822e-003 in [319] = -3.870851645947402e-003 in [320] = -3.597475533950260e-003 in [321] = -3.318857985461042e-003 in [322] = -3000422543655664e-003 in [323] = -2.658042081080524e-003 in [324] = -2.292813563887493e-003 in [325] = -1.919114790669928e-003 in [326] = -1.525818616748839e-003 in [327] = -1.156680209049319e-003 in [328] = - 7.804546272743493e-004 in [329] = -4.268579601396473e-004 in [330] = -1.324291707264515e-004 in [331] = 1.218226450050751e-004 in [332] = 3.1889336138130849e-004 in [333] ] = 4.749931197951235e-004 in [334] = 5.970696819774243e-004 in [335] = 6.673250213055329e-004 in [336] = 6.887783835812338e-004 in [337] = 6.766320515830324e-004 in [376] = -9.7677090655488747-004 in [376] = -9.294665200453614e-004 in [378] = -9.862027119530482e-004 in [379] = -1.047654674829846e-003 in [380] = -1.099000599887377e-003 in [381] = -1.151795860160292e- 003 in [382] = -1.194743370333155e-003 in [383] = -1.250742797799558e-003 in [384] = 1.287819050086379e-003 in [385] = 1.263569296641556e-003 in [386] = 1, 226113111394085e-003 in [387] = 1.177515087338257e-003 in [353] = 2.729136737522100e-003 in [354] = 2.703019498899013e-003 in [355] = 2.630471852319136e-003 in [356] = 2.470456304276468e-003 in [357] = 2,239142906871446e-003 in [358] = 2.033465291493264e-003 in [359] = 1.948069005335563e-003 in [360] = 1.725029670030533e-003 in [361] = 1.417366709895927e-003 in [362] = 1,127141815310061e-003 in [363] = 8.089811988213151e-004 in [364] = 4.708009521678285e-004 in [365] = 7.8882620739833088e-005 in [366] = -2.998739993995956e-004 in [367] = -4.733148292475610e-004 in [368] = -5.791145447913150e-004 in [369] = -6.754935404082003e-004 in [370] = -8.029620210721900e-004 in [371] = -9.726698841994444e-004 in [372] = -1.196637962311630e-003 in [373] = -1.292865844760059e-003 in [374] = -1.1426268465739874e-003 in [375] = -1.040598055074471e-003 in [414] = - 1.815837353167847e-004 in [415] = -3.595054179561440e-004 in [416] = -5.901617707607606e-007 in [417] = 1.831121301698088e-004 in [418] = 9.755685190624611e-005 in [418] ] = 6.606461762989423e-005 in [420] = 3.799971890923797e-005 in [421] = 4.1150075391929448e-005 in [422] = 5.021905476506264e-005 in [423] = 5.861800137939713e-005 in [424] = 2.126364641291926e-005 in [425] = 1,181077582797280e-004

100 in [388] = 1,122503050159859e-003 in [389] = 1.089428846944533e-003 in [390] = 1.054963366189962e-003 in [391] = 9.019128558297515e-004 in [392] = 7.897839620863715e-004 in [393] = 6,205675927856794e-004 in [394] = 3.157663628445906e-004 in [395] = 2.55644984493535844-004 in [396] = 2.520606580606257e-004 in [397] = 2.346980949474655e-004 in [398] = 2.060394037017961e-004 in [399] = 1.635905995590986e-004 in [400] = 1.176237128375623e-004 in [401] = 6.193369904730005e-005 in [402] = 3.568554800150508e-005 in [403] = 2.443161189273522e-005 in [404] = 1.334090914042349e-005 in [405] = 2.853437194757816e-006 in [406] = -1.039263591111469e-004 in [407] = 5.144969377044875e-005 in [408] = 9.711681816385056e-005 in [409] = 2.972023910553232e-005 in [410] = 5.397064424090302e-005 in [411] = 6.487880719449901e-005 in [412] = -5.192444140699947e-005 in [413] ] = -9.204876089551197e-005 in [452] = -1.728672507238372e-004 in [453] = -1.885286127508226e-004 in [454] = -2.078299015661617e-004 in [455] = -2.123671573189573e -004 in [456] = -2,415166002501312e-004 in [457] = -2.2217025956251449e-004 in [958] = -9.907630821710970e-005 in [459] = -8.039231481768845e-005 in [960] = -7.934509417722400e-005 in [426] = 9.990757789944374e-005 in [427] = 1.035782617124906e-004 in [428] = 8.870181895310037e-005 in [429] = 5.533953373249822e-005 in [430] = 1.580188994455254e-005 in [431] = 1.277184430250593e-006 in [432] = 5.009913312943629e-006 in [433] = 1.499170392246774e-005 in [434] = 2.241545750231630e-005 in [435] = 3.628511258723260e-005 in [436] = 2.406516798531014e-005 in [437] = 2.515118233957011e-005 in [438] = 3.759629789955498e-005 in [439] = 5.408154543124121e-005 in [440] = 4.493916063285122e-005 in [441] = 2.806963579578946e-005 in [442] = 2.364518513682831e-005 in [443] = 1.260639764582286e-005 in [444] = -2.599467772603631e-008 in [445] = -1.774108392496017e-005 in [446] ] = -5.889276659458115e-006 in [447] = -4.663777919108619e-005 in [448] = -2.078886359425321e-004 in [449] = -2.131405580107761e-004 in [450] = -1.784192600231068e -004 in [451] = -1,744841754193053e-004 in [490] = 4.939392400898679e-005 in [491] = 5.272982009116034e-005 in [492] = 4.005269212731273e-005 in [493] = 2.461876679726978e-005 in [494] = 4.469729032194765e-006 in [495] = 3.798519731621893e-007 in [496] = 1.374896222030490e-006 in [497] = 3.965363805500215e-006 in [498] = 7.300588863934780e-006

101 in [461] = -5.874199358780108e-005 in [462] = -5.449816072329412e-005 in [463] = -4.489491034408147e-005 in [464] = -3.498285982359981e-005 in [465] = - 1.748284921486958e-005 in [466] = -9.075430772832575e-006 in [467] = -1.052707430241351e-005 in [468] = -6.538878366985722e-006 in [469] = 2.206341308073472e-005 in [ 470] = 1,769261935287328e-004 in [471] = 6.418658561385058e-005 in [472] = -8.8882305312548962e-005 in [473] = -1.721347222211949e-005 in [474] = -6.093372716385583e 005 in [475] = -7.679955330373515e-005 in [476] = 7.194151087015007e-005 in [477] = 7.2245095937243279e-005 in [478] = 7.870354371072524e-005 in [479] = 5.822201682995846e-009 in [480] = 2.666444630171025e-004 in [481] = 7.872592352725688e-005 in [482] = 7.095886893185526e-005 in [483] = 5.643103068471008e-005 in [484] = 6.904415362098980e-005 in [485] = 4.694251739991356e-005 in [486] = 3.367998338617662e-005 in [487] = 6.481921021601837e-005 in [488] = 6.582328030188790e-005 in [489] = -4.256442530773449e-005 in [528] = -2.765649762593200e -007 in [529] = -1.922074581855119e-006 in [530] = -9.897194091136331e-007 in [531] = -7.873304717454037e-008 in [532] = 2.945239208477290e-008 in [533] = -2.757610624807679e-006 in [499] = 1.168894474770061e-005 in [500] = 8.563819899447630e-006 in [501] = 8.975977837330335e-006 in [502] = 2.800455533708622e-005 in [503] = 2.015445311139832e-005 in [504] = 1.125134651175812e-005 in [505] = 5.869707265615299e-006 in [506] = 1.013259758329981e-005 in [507] = 1.088325131492173e-005 in [508] = 7.167101260771279e-006 in [509] = 4.840577540089826e-006 in [510] = -1.469933448634890e-005 in [511] = -8.010079089953001e-006 in [512] = -3.299004046633323e-005 in [513] = -4.373302115187172e-005 [514] = -3.177468256997963e-005 in [515] = -2.976824036182567e-005 in [516] = -2.464228015326852e-005 in [517] = -1.606050838620834e-005 in [518] = -6 , 261944255489322e-006 in [519] = 4.591009581217994e-007 in [520] = 1.395220723090848e-005 in [521] = 1.622786214398703e-005 in [522] = -2.043464113212971e-006 in [523] = -1.653463907257247e-006 in [524] = -1.551250801467300e-008 in [525] = -1.907927361317977e-006 in [526] = -9.607068622268791e-007 in [527] = -4.636105364510011e-007 in [566] = 5.818594642226675e-006 in [567] = 2,150883991167946e-006 in [568] = 2.714879009950152e-007 in [569] = -2.567964804401197e-008 in [570] = 2.041128570435378e-006 in [571] = 3.262753594084781e-006

102

<td>in [534] = -1.402925247695813e-005</td><td>and [572]</td>

<td>in [535] = -9.388962780643742e-006</td><td>and [573]</td>

<td>in [536] = 2.068297421740023e-005</td><td>and [574]</td>

<td>in [537] = 1.496435902895210e-007</td><td>and [575]</td>

<td>in [538] = 6.757014945674924e-009</td><td>and [576]</td>

<td>in [539] = -2.778618354859861e-007</td><td>and [577]</td>

<td>in [540] = -1.569003268449803e-006</td><td>and [578]</td>

<td>in [541] = -1.089500601234349e-006</td><td>and [579]</td>

<td>in [542] = -9.870547653835426e-007</td><td>and [580]</td>

<td>in [543] = 3.867983283567218e-005</td><td>and [581]</td>

<td>in [544] = -1.232693496472088e-005</td><td>and [582]</td>

<td>in [545] = 9.464782951082177e-007</td><td>and [583]</td>

<td>in [546] = 8.254429452094225e-007</td><td>and [584]</td>

<td>in [547] = 4.883304950437536e-007</td><td>and [585]</td>

<td>in [548] = -2.066961713890010e-007</td><td>and [586]</td>

<td>in [549] = 5,158212471036245e-009</td><td>and [587]</td>

<td>in [550] = 2.267731106642486e-007</td><td>and [588]</td>

<td>in [551] = -4.880844550713951e-008</td><td>and [589]</td>

<td>in [552] = 3.361682183852576e-006</td><td>and [590]</td>

<td>in [553] = 4.677015459111491e-006</td><td>and [591]</td>

<td>in [554] = 2.820292122791583e-008</td><td>and [592]</td>

<td>in [555] = 5.143614846654519e-007</td><td>and [593]</td>

<td>in [556] = 3.818588614859347e-009</td><td>and [594]</td>

<td>in [557] = 1.737276553950212e-007</td><td>and [595]</td>

<td>in [558] = 1.876022048145804e-007</td><td>and [596]</td>

<td>in [559] = -2.986488593070417e-009</td><td>and [597]</td>

<td>in [560] = -1.409927495646886e-008</td><td>and [598]</td>

<td>in [561] = -6.977078748707401e-008</td><td>and [599]</td>

<td>in [562] = -1.280675520205100e-008</td><td>and [600]</td>

<td>in [563] = -2.222072007942510e-009</td><td>and [601]</td>

<td>in [564] = -1.775191290895584e-009</td><td>and [602]</td>

<td>in [565] = -1.686136654621906e-009</td><td>and [603]</td>

<td>in [604] = 1.070292712585309e-006</td><td></td>

<td>in [605] = 6.293002327021578e-007</td><td></td>

<td>in [606] = 3.575650976036433e-007</td><td></td>

3,567581483749161e-006

4,083718802566134e-006

5,364807253588177e-006

4,178050149840223e-006

5,189086332701670e-006

3,357218747491756e-006

6,310207878018869e-006

5,924001540927652e-006

5,161606640348293e-006

3,377814811795950e-006

1,323267689777069e-006

-1,074716688428712e-007

-3,561585382456484e-006

-4,518603099564185e-006

7,301956971603966e-007

5,891904775161025e-007

2,801882088134371e-008

6,322770332405526e-007

2,542598385847351e-007

1,272704908592385e-007

8,226599990523664e-008

5,433718768789140e-007

4,211177232106135e-007

3,552991527555180e-008

-1,398913109540774e-008

1,356727552196146e-006

-1,706941020342299e-005

1,013575160981381e-005

-2,285562946018590e-005

-8,908041185396514e-008

-9,597515277415496e-009

-3,225913527455964e-007

103 in [607] = 2.722295965060517e-005 in [608] = 8.676848186676888e-006 in [609] = 3.428660858940255e-007 in [610] = 4.767793949944890e-007 in [611] = 3.330981930777764e -3 in [612] = 2.399696144635756e-007 in [613] = 7.326611439066549e-009 in [614] = 1.349943693297681e-007 in [615] = -5.393555749348494e-008 in [616] = 3.629067065524143e 006 in [617] = -5.690530948134642e-006 in [618] = 1.387566465624550e-008 in [619] = 2.443085172403935e-007 in [620] = 1.723217058490933e-009 in [621] = 7.391973323448250 -008 in [622] = 5.303527922331415e-008 in [623] = -8.883499047404896e-010 in [624] = -3.870536804891648e-009 in [625] = -1.846547564287500e-008 in [626] = -4.244090917065736e-009 in [627] = -4.013524925634108e-009 in [628] = -6.325664562585882e-010 in [629] = -6.025110605409611e-010 in [630] = 1.620171502086309e-006 in [631] = 5.490569954646963e -007 in [632] = 6.355303179925355e-008 in [633] = -5.46597100684762e-009 in [634] = 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

104

Annex 2 [362] in [0] = 1.129580193872797e-002 in [1] | = 2.353059744904218e-002 in [2] | = 3.450718798721251e-002 in [3] | = 4.634695977000525e-002 in [4] | = 5.918677345174197e-002 in [5] | = 7.325978412117062e-002 in [6] = 8.829745229234007e-002 in [7] = 1.042033024802571e-001 in [8] | = 1.206924277410051e-001 in [9] | = 1.376149808913910e-001 in [10] | = 1.547461142258783e-001 in [11] | = 1.719726384566089e-001 in [12] | = 1.891590407342011e-001 in [13] | = 2.062605107774960e-001 in [14] | = 2,232276864673650e-001 in [15] | = 2,400768261284114e-001 in [16] | = 2.568176309566753e-001 in [17] | = 2.734977190313227e-001 in [18] = 2.901491317310591e-001 in [19] | = 3.068186515423912e-001 in [20] | = 3.235298682841570e-001 in [21] | = 3.403074196062977e-001 in [22] | = 3.571527896130669e-001 in [23] | = 3.790643979275026e-001 in [24] | = 3.910243970160607e-001 in [25] | = 4.080154903861317e-001 in [26] | = 4.250144186334534e-001 in [27] | = 4.420013942269341e-001 in [28] = 4.589582896978246e-001 in [29] | = 4,758753795532750e-001 in [36] | = 5.930981800982896e-001 in [37] | = 6.096690552916387e-001 in [38] | = 6.261725236758639e-001 in [39] | = 6.425939632009995e-001 in [40] | = 6.589148753746076e-001 in [41] | = 6.751199626157149e-001 in [42] | = 6.911981575264606e-001 in [43] | = 7.071447728928043e-001 in [44] | = 7.229599104052475e-001 in [45] | = 7.386515025302785e-001 in [46] | = 7.542294504292890e-001 in [47] | = 7.697093346240386e-001 in [48] | = 7.851012620144958e-001 in [49] | = 8.004165237845137e-001 in [50] | = 8,156523162880560e-001 in [51] | = 8.308039608112368e-001 in [52] | = 8.458450064727010e-001 in [53] | = 8.607492455327098e-001 in [54] | = 8.759640719350776e-001 in [55] | = 8.899474405744183e-001 in [56] | = 9.041286138017367e-001 in [57] | = 9.179666107725365e-001 in [58] | = 9.313879086278087e-001 in [59] | = 9.443802853939540e-001 in [60] | = 9.568885413848645e-001 in [61] | = 9.690016637782843e-001 in [62] | = 9.807691702375303e-001 in [63] | = 9.927543720639498e-001 in [64] | = 1.001463112557766e + 000 in [65] | = 1,006893331637123e + 000 in [66] = 1.012508393574432e + 000 in [67] | = 1.017729040219375e + 000

105 in [30] = 4.927463828072591e-001 in [31] = 5.095720854151864e-001 in [32] | = 5.263554446856779e-001 in [33] | = 5.430990601899994e-001 in [34] | = 5.598052330684253e-001 in [35] | = 5.764734796907189e-001 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 [79] | = 1.041043184216171e + 000 in [80] | = 1.040262316588456e + 000 in [81] | = 1.039061496136853e + 000 in [82] | = 1,037422300157921e + 000 in [83] | = 1.035311720204252e + 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] | = 9.608519516143015e-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 [68] | = 1.022470190536100e + 000 in [69] | = 1.026615653698808e + 000 in [70] | = 1.030198648769593e + 000 in [71] | = 1.033205850580933e + 000 in [72] | = 1.035694432087486e + 000 in [73] | = 1.037683165297586e + 000 in [112] | = 7.609051036128973e-001 in [113] | = 7.445111681431031e-001 in [114] | = 7,298745530879272e-001 in [115] | = 7.140087729493950e-001 in [116] | = 6.979336851549095e-001 in [117] | = 6.816667882498023e-001 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] | = 5.811992722116214e-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] | = 4.609828932783459e-001 in [131] | = 4.437530233023859e-001 in [132] | = 4.265950246465440e-001 in [133] | = 4.095160967543179e-001 in [134] | = 3.925409172155113e-001 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

106

<td>| in [103]</td><td>= 8.859232320517536e-001</td><td>in [141]</td><td>= 2.779637821990255e-001</td>

<td>| in [104]</td><td>= 8.734366852542127e-001</td><td>in [142]</td><td>= 2.623749159488041e-001</td>

<td>| in [105]</td><td>= 8.605542791988831e-001</td><td>in [143]</td><td>= 2.470098299603623e-001</td>

<td>| in [106]</td><td>= 8.4472987145504696e-001</td><td>in [144]</td><td>= 2.318815478758375e-001</td>

<td>| in [107]</td><td>= 8.336863467961255e-001</td><td>in [145]</td><td>= 2.169925682529340e-001</td>

<td>| in [108]</td><td>= 8.197387292306723e-001</td><td>in [146]</td><td>= 2.023548005388463e-001</td>

<td>| in [109]</td><td>= 8.054701312929008e-001</td><td>in [147]</td><td>= 1.879711746686855e-001</td>

<td>| in [110]</td><td>= 7.908995350037713e-001</td><td>in [148]</td><td>= 1.738542127021508e-001</td>

<td>| in [111]</td><td>= 7.760385598209244e-001</td><td>in [149]</td><td>= 1.600061812296078e-001</td>

<td>| in [150]</td><td>= 1.464389150679625e-001</td><td>in [188]</td><td>= 1.261262023246478e-001</td>

<td>| in [151]</td><td>= 1.331549923127771e-001</td><td>in [189]</td><td>= 1.268280540744526e-001</td>

<td>| in [152]</td><td>= 1.201628679722633e-001</td><td>in [190]</td><td>= 1.272498700590511e-001</td>

<td>| in [153]</td><td>= 1.074630704470568e-001</td><td>in [191]</td><td>= 1.273590703506806e-001</td>

<td>| in [154]</td><td>= 9.506966959632511e-002</td><td>in [192]</td><td>= 1.274567595465545e-001</td>

<td>| in [155]</td><td>= 8.298103104739203e-002</td><td>in [193]</td><td>= 1.275561350483646e-001</td>

<td>| in [156]</td><td>= 7.120356992726613e-002</td><td>in [194]</td><td>= 1.273648326872248e-001</td>

<td>| in [157]</td><td>= 5.973741829536090e-002</td><td>in [195]</td><td>= 1.269415772180714e-001</td>

<td>| in [158]</td><td>= 4.859005767016811e-002</td><td>in [196]</td><td>= 1.262995646340671e-001</td>

<td>| in [159]</td><td>= 3.775928110298274e-002</td><td>in [197]</td><td>= 1.254605188749804e-001</td>

<td>| in [160]</td><td>= 2.726484300186575e-002</td><td>in [198]</td><td>= 1.244269583009826e-001</td>

<td>| in [161]</td><td>= 1.711323992709580e-002</td><td>in [199]</td><td>= 1.232131583108813e-001</td>

<td>| in [162]</td><td>= 7.298197371320593e-003</td><td>in [200]</td><td>= 1.218183974842866e-001</td>

<td>| in [163]</td><td>= 2.184256929356781e-003</td><td>in [201]</td><td>= 1.202545652840080e-001</td>

<td>| in [164]</td><td>= 1.132324047372148e-002</td><td>in [202]</td><td>= 1.185243106889108e-001</td>

<td>| in [165]</td><td>= 2.012236990754980e-002</td><td>in [203]</td><td>= 1.166399102636992e-001</td>

<td>| in [166]</td><td>= 2.857528272530154e-002</td><td>in [204]</td><td>= 1.146042249339280e-001</td>

<td>| in [167]</td><td>= 3.666942822678171e-002</td><td>in [205]</td><td>= 1.124296184976912e-001</td>

<td>| in [168]</td><td>= 4.439683978044157e-002</td><td>in [206]</td><td>= 1.101215600923314e-001</td>

<td>| in [169]</td><td>= 5.177964768870787e-002</td><td>in [207]</td><td>= 1.076972053405737e-001</td>

<td>| in [170]</td><td>= 5.881296711410786e-002</td><td>in [208]</td><td>= 1.051641975499523e-001</td>

<td>| in [171]</td><td>= 6.550209046893848e-002</td><td>in [209]</td><td>= 1.025397604985405e-001</td>

<td>| in [172]</td><td>= 7.184073822817207e-002</td><td>in [210]</td><td>= 9.982957934346254e-002</td>

<td>| in [173]</td><td>= 7.783299328224960e-002</td><td>in [211]</td><td>= 9.705239536075722e-002</td>

<td>| in [174]</td><td>= 8.347150698567406e-002</td><td>in [212]</td><td>= 9.421624116597689e-002</td>

<td>| in [175]</td><td>= 8.875756217893037e-002</td><td>in [213]</td><td>= 9.133590931873967e-002</td>

107

<td>| in [176]</td><td>= 9.368651761350569e-002</td><td>in [219]</td><td>= 8.841813387276727e-002</td>

<td>| in [177]</td><td>= 9.826251129465624e-002</td><td>in [215]</td><td>= 8.547715661443602e-002</td>

<td>| in [178]</td><td>= 1.024804711677230e-001</td><td>in [216]</td><td>= 8.2251962055343706e-002</td>

<td>| in [179]</td><td>= 1.063454554357498e-001</td><td>in [217]</td><td>= 7.955570759229536e-002</td>

<td>| in [180]</td><td>= 1.098551252869576e-001</td><td>in [218]</td><td>= 7.657649751612349e-002</td>

<td>| in [181]</td><td>= 1.130180022553412e-001</td><td>in [219]</td><td>= 7.360559211914287e-002</td>

<td>| in [182]</td><td>= 1.158358935177899e-001</td><td>in [220]</td><td>= 7.064948295960993e-002</td>

<td>| in [183]</td><td>= 1.183233335449968e-001</td><td>in [221]</td><td>= 6.771675107480543e-002</td>

<td>| in [184]</td><td>= 1.204854506722672e-001</td><td>in [222]</td><td>= 6.480448458935215e-002</td>

<td>| in [185]</td><td>= 1.223371395264402e-001</td><td>in [223]</td><td>= 6.192692754258131e-002</td>

<td>| in [186]</td><td>= 1.238868653862843e-001</td><td>in [224]</td><td>= 5.911363299658311e-002</td>

<td>| in [187]</td><td>= 1.251477258491527e-001</td><td>in [225]</td><td>= 5.637219228757212e-002</td>

<td>| in [226]</td><td>= 5.368313072095600e-002</td><td>in [264]</td><td>= 5.063851046064050e-003</td>

<td>| in [227]</td><td>= 5,105620793438655e-002</td><td>in [265]</td><td>= 4.754191853611012e-003</td>

<td>| in [228]</td><td>= 4.849284995895640e-002</td><td>in [266]</td><td>= 4.448993249380505e-003</td>

<td>| in [229]</td><td>= 4.599068181839981e-002</td><td>in [267]</td><td>= 4.133639756278191e-003</td>

<td>| in [230]</td><td>= 4.355568588898841e-002</td><td>in [268]</td><td>= 3.811612348723333e-003</td>

<td>| in [231]</td><td>= 4.125570251909672e-002</td><td>in [269]</td><td>= 3.505531318950422e-003</td>

<td>| in [232]</td><td>= 3.907137550527191e-002</td><td>in [270]</td><td>= 3.209092846617964e-003</td>

<td>| in [233]</td><td>= 3.696342556744636e-002</td><td>in [271]</td><td>= 2.927159436740159e-003</td>

<td>| in [234]</td><td>= 3.493300140502248e-002</td><td>in [272]</td><td>= 2.653818578698405e-003</td>

<td>| in [235]</td><td>= 3.298151059524886e-002</td><td>in [273]</td><td>= 2.396404013961463e-003</td>

<td>| in [236]</td><td>= 3.110861245410919e-002</td><td>in [279]</td><td>= 2.152379960589273e-003</td>

<td>| in [237]</td><td>= 2.931525594774175e-002</td><td>in [275]</td><td>= 1.924844672908215e-003</td>

<td>| in [238]</td><td>= 2.760090729801069e-002</td><td>in [276]</td><td>= 1.699160580023900e-003</td>

<td>| in [239]</td><td>= 2.597956638848436e-002</td><td>in [277]</td><td>= 1.480542563288228e-003</td>

<td>| in [240]</td><td>= 2.443433592149451e-002</td><td>in [278]</td><td>= 1.283280633901446e-003</td>

<td>| in [241]</td><td>= 2.296470793543091e-002</td><td>in [279]</td><td>= 1.131859661378862e-003</td>

<td>| in [242]</td><td>= 2.156304510969632e-002</td><td>in [280]</td><td>= 9.730460256556873e-004</td>

<td>| in [243]</td><td>= 2.023524610221679e-002</td><td>in [281]</td><td>= 7.677634115875747e-004</td>

<td>| in [244]</td><td>= 1.897505817503749e-002</td><td>in [282]</td><td>= 5.599347984905645e-004</td>

<td>| in [245]</td><td>= 1.778248750467421e-002</td><td>in [283]</td><td>= 3.337966579125254e-004</td>

<td>| in [246]</td><td>= 1.665187994388476e-002</td><td>in [284]</td><td>= 9.099722643476421e-005</td>

<td>| in [247]</td><td>= 1.557759513377242e-002</td><td>in [285]</td><td>= 1.498231621816041e-004</td>

<td>| in [248]</td><td>= 1.456208586604537e-002</td><td>in [286]</td><td>= 4.366447012116811e-004</td>

108

<td>| in [249]</td><td>= 1.361072086117313e-002</td><td>in [287]</td><td>= 6.307841647560053e-004</td>

<td>| in [250]</td><td>= 1.270747042064656e-002</td><td>in [288]</td><td>= 6.150316826138937e-004</td>

<td>| in [251]</td><td>= 1.186210743261470e-002</td><td>in [289]</td><td>= 8.990255827053560e-004</td>

<td>| in [252]</td><td>= 1.106958962776399e-002</td><td>in [290]</td><td>= 1.232134364570107e-003</td>

<td>| in [253]</td><td>= 1.033126278863177e-002</td><td>in [291]</td><td>= 1.471167206249042e-003</td>

<td>| in [254]</td><td>= 9.640298325700842e-003</td><td>in [292]</td><td>= 1.697652664777771e-003</td>

<td>| in [255]</td><td>= 8.996371481700806e-003</td><td>in [293]</td><td>= 1.985825255428654e-003</td>

<td>| in [256]</td><td>= 8,407748878436545e-003</td><td>in [294]</td><td>= 2.172866052963961e-003</td>

<td>| in [257]</td><td>= 7.887393114319395e-003</td><td>in [295]</td><td>= 1.812176023993582e-003</td>

<td>| in [258]</td><td>= 7.380543918629573e-003</td><td>in [296]</td><td>= 1.344657262814793e-003</td>

<td>| in [259]</td><td>= 6.925141135202262e-003</td><td>in [297]</td><td>= 9.373975348172919e-004</td>

<td>| in [260]</td><td>= 6.500502521462604e-003</td><td>in [298]</td><td>= 5.621720998949145e-004</td>

<td>| in [261]</td><td>= 6,109178606718115e-003</td><td>in [299]</td><td>= 2.048498552413189e-004</td>

<td>| in [262]</td><td>= 5.741103163221257e-003</td><td>in [300]</td><td>= 2.004822830002534e-004</td>

<td>| in [263]</td><td>= 5.399569608919965e-003</td><td>in [301]</td><td>= 6.169854804735951e-004</td>

<td>| in [302]</td><td>= 1.061498982103114e-003</td><td>in [340]</td><td>= 7.154123487609100e-004</td>

<td>| in [303]</td><td>= 1.594860949611097e-003</td><td>in [341]</td><td>= 7.376101027486600e-004</td>

<td>| in [304]</td><td>= 2.124647831574725e-003</td><td>in [342]</td><td>= 6.976561203768226e-004</td>

<td>| in [305]</td><td>= 2.621537051750861e-003</td><td>in [343]</td><td>= 5.721223454434728e-004</td>

<td>| in [306]</td><td>= 3.064311083207632e-003</td><td>in [344]</td><td>= 2.934875643581191e-004</td>

<td>| in [307]</td><td>= 3.460362845825662e-003</td><td>in [345]</td><td>= 1.092526149391273e-004</td>

<td>| in [308]</td><td>= 3.794425324215804e-003</td><td>in [346]</td><td>= 6.415402443848103e-004</td>

<td>| in [309]</td><td>= 4.091032597247918e-003</td><td>in [347]</td><td>= 1.194730618383423e-003</td>

<td>| in [310]</td><td>= 4.369553676668050e-003</td><td>in [348]</td><td>= 1.557112059887280e-003</td>

<td>| in [311]</td><td>= 4.554811297024067e-003</td><td>in [349]</td><td>= 1.891971801393744e-003</td>

<td>| in [312]</td><td>= 4.663276675479689e-003</td><td>in [350]</td><td>= 2.225524159129023e-003</td>

<td>| in [313]</td><td>= 4.722567636185647e-003</td><td>in [351]</td><td>= 2.530906981099261e-003</td>

<td>| in [314]</td><td>= 4.704321497976561e-003</td><td>in [352]</td><td>= 2.719749515067397e-003</td>

<td>| in [315]</td><td>= 4.636227793039124e-003</td><td>in [353]</td><td>= 2.729136737522100e-003</td>

<td>| in [316]</td><td>= 4.517190210387324e-003</td><td>in [354]</td><td>= 2.703019498899013e-003</td>

<td>| in [317]</td><td>= 4.351667566540186e-003</td><td>in [355]</td><td>= 2.630471852319136e-003</td>

<td>| in [318]</td><td>= 4.135130493071822e-003</td><td>in [356]</td><td>= 2.470456304276468e-003</td>

<td>| in [319]</td><td>= 3.870851645947402e-003</td><td>in [357]</td><td>= 2.239142906871446e-003</td>

<td>| in [320]</td><td>= 3.5597475533950260e-003</td><td>in [358]</td><td>= 2.033465291493264e-003</td>

<td>| in [321]</td><td>= 3.318857985461042e-003</td><td>in [359]</td><td>= 1.948069005335563e-003</td>

109

<td>| in [322]</td><td>= 3.000422543655664e-003</td><td>in [360]</td><td>= 1.725029670030533e-003</td>

<td>| in [323]</td><td>= 2.658042081080524e-003</td><td>in [361]</td><td>= 1.417366709895927e-003</td>

<td>| in [324]</td><td>= 2.292813563887493e-003</td><td>in [362]</td><td>= 1.127141815310061e-003</td>

<td>| in [325]</td><td>= 1.914114740669928e-003</td><td>in [363]</td><td>= 8.089811988213151e-004</td>

<td>| in [326]</td><td>= 1.525818616748839e-003</td><td>in [364]</td><td>= 4.708009521678285e-004</td>

<td>| in [327]</td><td>= 1.156680209049319e-003</td><td>in [365]</td><td>= 7.882620739833088e-005</td>

<td>| in [328]</td><td>= 7.804546272743493e-004</td><td>in [366]</td><td>= 2.998739993995956e-004</td>

<td>| in [329]</td><td>= 4.268574601396473e-004</td><td>in [367]</td><td>= 4.733148292475610e-004</td>

<td>| in [330]</td><td>= 1.324291707264515e-004</td><td>in [368]</td><td>= 5.791145447913150e-004</td>

<td>| in [331]</td><td>= 1.218226450050751e-004</td><td>in [369]</td><td>= 6.754935404082003e-004</td>

<td>| in [332]</td><td>= 3.189336138130849e-004</td><td>in [370]</td><td>= 8.029620210721900e-004</td>

<td>| in [333]</td><td>= 4.749931197951235e-004</td><td>in [371]</td><td>= 9.726698841994444e-004</td>

<td>| in [339]</td><td>= 5.970696819774243e-004</td><td>in [372]</td><td>= 1.196637962311630e-003</td>

<td>| in [335]</td><td>= 6.673250213055329e-004</td><td>in [373]</td><td>= 1.292865844760059e-003</td>

<td>| in [336]</td><td>= 6.887783835812338e-004</td><td>in [374]</td><td>= 1.146268465739874e-003</td>

<td>| in [337]</td><td>= 6.766320515830324e-004</td><td>in [375]</td><td>= 1.040598055074471e-003</td>

<td>| in [338]</td><td>= 6.944123176012471e-004</td><td>in [376]</td><td>= 9.767709065548874e-004</td>

<td>| in [339]</td><td>= 7.139919634325070e-004</td><td>in [377]</td><td>= 9.294665200453614e-004</td>

<td>| in [378]</td><td>= 9.862027119530482e-004</td><td>in [416]</td><td>= 5.901617707607606e-007</td>

<td>| in [379]</td><td>= 1.047654674829846e-003</td><td>in [417]</td><td>= 1.831121301698088e-004</td>

<td>| in [380]</td><td>= 1.099000599887377e-003</td><td>in [418]</td><td>= 9.755685190624611e-005</td>

<td>| in [381]</td><td>= 1.151795860160292e-003</td><td>in [419]</td><td>= 6.606461762989423e-005</td>

<td>| in [382]</td><td>= 1.194743370333155e-003</td><td>in [420]</td><td>= 3.799971890923797e-005</td>

<td>| in [383]</td><td>= 1.250742797799558e-003</td><td>in [421]</td><td>= 4.150075391929448e-005</td>

<td>| in [384]</td><td>= 1.287819050086379e-003</td><td>in [422]</td><td>= 5.021905476506264e-005</td>

<td>| in [385]</td><td>= 1.263569296641556e-003</td><td>in [423]</td><td>= 5.861800137434713e-005</td>

<td>| in [386]</td><td>= 1.226113111394085e-003</td><td>in [424]</td><td>= 2.1266364641291926e-005</td>

<td>| in [387]</td><td>= 1.177515087338257e-003</td><td>in [425]</td><td>= 1.181077582797280e-004</td>

<td>| in [388]</td><td>= 1.122503050159859e-003</td><td>in [426]</td><td>= 9.990757789944374e-005</td>

<td>| in [389]</td><td>= 1.089428846944533e-003</td><td>in [427]</td><td>= 1.035782617124906e-004</td>

<td>| in [390]</td><td>= 1.054963366189962e-003</td><td>in [428]</td><td>= 8.870181845310037e-005</td>

<td>| in [391]</td><td>= 9.019128558297515e-004</td><td>in [429]</td><td>= 5.533953373249822e-005</td>

<td>| in [392]</td><td>= 7.847839620863715e-004</td><td>in [430]</td><td>= 1.580188994455254e-005</td>

<td>| in [393]</td><td>= 6.205675927856794e-004</td><td>in [931]</td><td>= 1.277184430250593e-006</td>

<td>| in [394]</td><td>= 3.157663628445906e-004</td><td>in [432]</td><td>= 5.009913312943629e-006</td>

110

<td>| in [395]</td><td>| = 2.556449844935384e-004</td><td>in [433]</td>

<td>| in [396]</td><td>| = 2.520606580606257e-004</td><td>in [434]</td>

<td>| in [397]</td><td>| = 2.346980949474655e-004</td><td>in [435]</td>

<td>| in [398]</td><td>| = 2.060394037017961e-004</td><td>in [436]</td>

<td>| in [399]</td><td>| = 1.635905995590986e-004</td><td>in [437]</td>

<td>| in [400]</td><td>| = 1.176237128375623e-004</td><td>in [438]</td>

<td>| in [401]</td><td>| = 6.193369904730005e-005</td><td>in [439]</td>

<td>| in [402]</td><td>| = 3.568554800150508e-005</td><td>in [440]</td>

<td>| in [403]</td><td>| = 2.443161189273522e-005</td><td>in [441]</td>

<td>| in [404]</td><td>| = 1.334090914042349e-005</td><td>in [442]</td>

<td>| in [405]</td><td>| = 2.853437194757816e-006</td><td>in [443]</td>

<td>| in [406]</td><td>| = 1.039263591111469e-004</td><td>in [444]</td>

<td>| in [407]</td><td>| = 5.144969377044875e-005</td><td>in [445]</td>

<td>| in [408]</td><td>| = 9.711681816385056e-005</td><td>in [446]</td>

<td>| in [409]</td><td>| = 2.472023910553232e-005</td><td>in [447]</td>

<td>| in [410]</td><td>| = 5.397064424090302e-005</td><td>in [448]</td>

<td>| in [411]</td><td>| = 6.987880719449901e-005</td><td>in [449]</td>

<td>| in [412]</td><td>| = 5.192444140699947e-005</td><td>in [450]</td>

<td>| in [413]</td><td>| = 9.204876089551197e-005</td><td>in [451]</td>

<td>| in [114]</td><td>| = 1.815837353167847e-004</td><td>in [952]</td>

<td>| in [415]</td><td>| = 3.595054179561440e-004</td><td>in [453]</td>

<td>| in [454]</td><td>= 2.078299015661617e-004</td><td>in [492] |</td>

<td>| in [455] |</td><td>= 2.123671573189573e-004</td><td>in [493]</td>

<td>| in [456] |</td><td>= 2.415166002501312e-004</td><td>in [999]</td>

<td>| in [957]</td><td>= 2.217025456251999e-009</td><td>in [495]</td>

<td>| in [458] |</td><td>= 9.907630821710970e-005</td><td>in [496]</td>

<td>| in [459]</td><td>= 8.039231481768845e-005</td><td>in [997]</td>

<td>| in [960] |</td><td>= 7.934509417722400e-005</td><td>in [498]</td>

<td>| in [961] |</td><td>= 5.874199358780108e-005</td><td>in [499]</td>

<td>| in [462]</td><td>= 5.449816072329912e-005</td><td>in [500] |</td>

<td>| in [463]</td><td>= 4.489491034408147e-005</td><td>in [501] |</td>

<td>| in [464] |</td><td>= 3.498285982359981e-005</td><td>in [502]</td>

<td>| in [465] |</td><td>= 1.748289921486958e-005</td><td>in [503] |</td>

<td>| in [466]</td><td>= 9.075430772832575e-006</td><td>in [504]</td>

<td>| in [467] |</td><td>= 1.052707430241351e-005</td><td>in [505]</td>

= 1.499170392246774e-005 = 2.241545750231630e-005 = 3.628511258723260e-005 = 2.406516798531014e-005 = 2.515118233957011e-005 = 3.759629789955498e-005 = 5.408154543124121e-00e = 0040 = , 806963579578946e-005 = 2.364518513682831e-005 = 1.260639764582286e-005 = 2.599467772603631e-008 = 1.774108392496017e-005 = 5.889276659458115e-006 = 4.6637778619946267888888888e8e -004 = 1.784192600231068e-004 = 1.744841754193053e-004 = 1.728672507238372e-004 = 1.885286127508226e-004 = 4.005269212731273e-005 = 2.461876679726978e-005 = 9.969729032199765e-006 = 3.798519731621893e-007 = 1.374896222030490e-006 = 3.965365806 006343.3008806 006347.300 , 168894474770061e-005 = 8.563819899447630e-006 = 8.975977837330335e-006 = 2.800455533708622e-005 = 2.015945311139832e-005 = 1.125134651175812e-005 = 5.869707265615299e-005

111

<td>| and [468]</td><td>= 6.538878366985722e-006</td><td>and [506]</td><td>= 1.013259758329981e-005</td>

<td>| and [469]</td><td>= 2.206341308073472e-005</td><td>and [507]</td><td>= 1.088325131492173e-005</td>

<td>| and [470]</td><td>= 1.769261935287328e-004</td><td>and [508]</td><td>= 7.167101260771279e-006</td>

<td>| and [471]</td><td>= 6.418658561385058e-005</td><td>and [509]</td><td>= 4.840577540089826e-006</td>

<td>| and [972]</td><td>= 8.8882305312548962e-005</td><td>and [510]</td><td>= 1.469933448634890e-005</td>

<td>| and [473]</td><td>= 1.721347222211949e-005</td><td>and [511]</td><td>= 8.010079089953001e-006</td>

<td>| and [974]</td><td>= 6.093372716385583e-005</td><td>and [512]</td><td>= 3.299004046633323e-005</td>

<td>| and [975]</td><td>= 7.679955330373515e-005</td><td>and [513]</td><td>= 4.373302115187172e-005</td>

<td>| and [476]</td><td>= 7.194151087015007e-005</td><td>and [514]</td><td>= 3.177468256997963e-005</td>

<td>| and [477]</td><td>= 7.295095937293279e-005</td><td>and [515]</td><td>= 2.976824036182567e-005</td>

<td>| and [478]</td><td>= 7.870359371072524e-005</td><td>and [516]</td><td>= 2.464228015326852e-005</td>

<td>| and [479]</td><td>= 5.822201682995846e-004</td><td>and [517]</td><td>= 1.606050838620834e-005</td>

<td>| and [480]</td><td>= 2.666444630171025e-004</td><td>and [518]</td><td>= 6.261944255489322e-006</td>

<td>| and [481]</td><td>= 7.872592352725688e-005</td><td>and [519]</td><td>= 9.591009581217999e-007</td>

<td>| and [482]</td><td>= 7.095886893185526e-005</td><td>and [520]</td><td>= 1.395220723090848e-005</td>

<td>| and [483]</td><td>= 5.693103068971008e-005</td><td>and [521]</td><td>= 1.622786214398703e-005</td>

<td>| and [484]</td><td>= 6.904415362098980e-005</td><td>and [522]</td><td>= 2.043469113212971e-006</td>

<td>| and [485]</td><td>= 4.694251739991356e-005</td><td>and [523]</td><td>= 1.653963907257297e-006</td>

<td>| and [986]</td><td>= 3.367998338617662e-005</td><td>and [524]</td><td>= 1.551250801967300e-008</td>

<td>| and [487]</td><td>= 6.481921021601837e-005</td><td>and [525]</td><td>= 1.907927361317977e-006</td>

<td>| and [488]</td><td>= 6.582328030188790e-005</td><td>and [526]</td><td>= 9.607068622268791e-007</td>

<td>| and [489]</td><td>= 4.256442530773449e-005</td><td>and [527]</td><td>= 4.636105364510011e-007</td>

<td>| and [490]</td><td>= 4.939392400898679e-005</td><td>and [528]</td><td>= 2.765699762593200e-007</td>

<td>| and [491]</td><td>= 5.272982009116039e-005</td><td>and [529]</td><td>= 1.922074581855119e-006</td>

<td>| and [530]</td><td>= 9.897199091136331e-007</td><td>and [568]</td><td>= 2.714879009950152e-007</td>

<td>| and [531]</td><td>= 7.873309717459037e-008,</td><td>and [569]</td><td>= 2.567969809401197e-008</td>

<td>| and [532]</td><td>= 2.945239208477290e-008</td><td>and [570]</td><td>= 2.091128570435378e-006</td>

<td>| and [533]</td><td>= 2.757610624807679e-006</td><td>and [571]</td><td>= 3.262753594084781e-006</td>

<td>| and [534]</td><td>= 1.402925247695813e-005</td><td>and [572]</td><td>= 3.567581483749161e-006</td>

<td>| and [535]</td><td>= 9.38962780643742e-006</td><td>and [573]</td><td>= 4.083718802566134e-006</td>

<td>| and [536]</td><td>= 2.068297.421740023e-005</td><td>and [574]</td><td>= 5.364807253588177e-006</td>

<td>| and [537]</td><td>= 1.496435902895210e-007</td><td>and [575]</td><td>= 4.178050149840223e-006</td>

<td>| and [538]</td><td>= 6.757014945674924e-009</td><td>and [576]</td><td>= 5.189086332701670e-006</td>

<td>| and [539]</td><td>= 2.778618354859861e-007</td><td>and [577]</td><td>= 3.357218747491756e-006</td>

<td>| and [590]</td><td>= 1.569003268499803e-006</td><td>and [578]</td><td>= 6.310207878018869e-006</td>

112

<td>| and [591]</td><td>= 1.089500601234349e-006</td><td>and [579]</td><td>= 5.924001540927652e-006</td>

<td>| and [542]</td><td>= 9.870547653835426e-007</td><td>and [580]</td><td>= 5.161606640348293e-006</td>

<td>| and [543]</td><td>= 3.867483283567218e-005</td><td>and [581]</td><td>= 3.377814811745950e-006</td>

<td>| and [544]</td><td>= 1.232693496472088e-005</td><td>and [582]</td><td>= 1.323267689777069e-006</td>

<td>| w (545]</td><td>= 9.464782951082177e-007</td><td>and [583]</td><td>= 1.079716688428712e-007</td>

<td>| and [546]</td><td>= 8.254429452094225e-007</td><td>and [584]</td><td>= 3.561585382456489e-006</td>

<td>| and [547]</td><td>= 4.883304950937536e-007</td><td>and [585]</td><td>= 4.518603099564185e-006</td>

<td>| and [598]</td><td>= 2.066961713890010e-007</td><td>and [586]</td><td>= 7.301956971603966e-007</td>

<td>| and [549]</td><td>= 5.158212471036245e-009</td><td>and [587]</td><td>= 5.891904775161025e-007</td>

<td>| and [550]</td><td>= 2.267731106642986e-007</td><td>and [588]</td><td>= 2.801882088134371e-008</td>

<td>| and [551]</td><td>= 4.880844550713951e-008</td><td>and [589]</td><td>= 6.322770332405526e-007</td>

<td>| and [552]</td><td>= 3.361682183852576e-006</td><td>and [590]</td><td>= 2.542598385847351e-007</td>

<td>| and [553]</td><td>= 9.677015459111491e-006</td><td>and [591]</td><td>= 1.272704908592385e-007</td>

<td>| and [554]</td><td>= 2.820292122791583e-008</td><td>and [592]</td><td>= 8.226599990523664e-008</td>

<td>| and [555]</td><td>= 5.143614846654519e-007</td><td>and [593]</td><td>= 5.433718768789140e-007</td>

<td>| and [556]</td><td>= 3.818588614859347e-009</td><td>and [599]</td><td>= 4.211177232106135e-007</td>

<td>| and [557]</td><td>= 1.737276553950212e-007</td><td>and [595]</td><td>= 3.552991527555180e-008</td>

<td>| and [558]</td><td>= 1.876022048145804e-007</td><td>and [596]</td><td>= 1.398913109540774e-008</td>

<td>| and [559]</td><td>= 2.986488593070417e-009</td><td>and [597]</td><td>= 1.356727552196146e-006</td>

<td>| and [560]</td><td>= 1.409927495646886e-008</td><td>and [598]</td><td>= 1.706991020392299e-005</td>

<td>| and [561]</td><td>= 6.977078748707401e-008</td><td>and [599]</td><td>= 1.013575160981381e-005</td>

<td>| and [562]</td><td>= 1.280675520205100e-008</td><td>and [600]</td><td>= 2.285562946018590e-005</td>

<td>| and [563]</td><td>= 2.222072007942510e-009</td><td>and [601]</td><td>= 8.908041185396519e-008</td>

<td>| and [564]</td><td>= 1.775191290895584e-009</td><td>and [602]</td><td>= 9.597515277415996e-009</td>

<td>| and [565]</td><td>= 1.686136654621906e-009</td><td>and [603]</td><td>= 3.225913527455964e-007</td>

<td>| and [566]</td><td>= 5.818594642226675e-006</td><td>and [609]</td><td>= 1.070242712585309e-006</td>

<td>| and [567]</td><td>= 2,150883991167946e-006</td><td>and [605]</td><td>= 6.293002327021578e-007</td>

<td>| and [606]</td><td>= 3.575650976036433e-007</td><td></td><td></td>

<td>| and [607]</td><td>= 2.722295965060517e-005</td><td></td><td></td>

<td>| and [608]</td><td>= 8.676848186676888e-006</td><td></td><td></td>

<td>| and [609]</td><td>= 3.428660858940255e-007</td><td></td><td></td>

<td>| and [610]</td><td>= 4.767793999949890e-007</td><td></td><td></td>

<td>| and [611]</td><td>= 3.330981930777764e-007</td><td></td><td></td>

<td>| and [612]</td><td>= 2.399696144635756e-007</td><td></td><td></td>

<td>| and [613]</td><td>= 7.326611439066549e-009</td><td></td><td></td>

113 in [614] = 1.349943693297681e-007 in [615] | = 5.393555749348494e-008 in [616] = 3.629067065524143e-006 in [617] | = 5.690530948134642e-006 in [618] = 1.387566965629550e-008 in [619] | = 2.443085172403935e-007 in [620] | = 1.723217058490933e-009 in [621] | = 7.3391973323448250e-008 in [622] | = 5.303527922331415e-008 in [623] | = 8.883499047404846e-010 in [624] | = 3.870536804891648e-009 in [625] | = 1.846547564287500e-008 in [626] | = 4.244090917065736e-009 in [627] = 4.013524925634108e-009 in [628] | = 6,325664562585882e-010 in [629] = 6.025110605409611e-010 in [630] | = 1.620171502086309e-006 in [631] | = 5.490569954646963e-007 in [632] | = 6.355303179925355e-008 in [633] = 5.426597100684762e-009 in [634] | = 4.292861814899369e-007 in [635] | = 6.834209542421138e-007 in [636] | = 7.0996330149958 63e-007 in [637] | = 8.109951846981774e-007 in [638] | = 4.118359768898598e-007 in [639] | = 6.571760029213382e-007

Annex 3 [363]

0.010 &lt;in [0] &lt;0.012 0.023 &lt;in [1] &lt;0.025 0.034 &lt;in [2] &lt;0.036

0.592 &lt;in [36] &lt;0.594 0.609 &lt;in [37] &lt;0.611 0.625 &lt;in [38] &lt;0.627 0.642 &lt;in [39] &lt;0.644 0.658 &lt;in [40] &lt;0.660

114

<td>0.045 &lt;in [3] &lt;0.047</td><td>0.674 &lt;in [41] &lt;0.676</td>

<td>0.058 &lt;in [4] &lt;0.060</td><td>0.690 &lt;in [92] &lt;0.692</td>

<td>0.072 &lt;in [5] &lt;0.074</td><td>0.706 &lt;in [43] &lt;0.708</td>

<td>0.087 &lt;in [6] &lt;0.089</td><td>0.722 &lt;in [44] &lt;0.724</td>

<td>0.103 &lt;in [7] &lt;0.105</td><td>0.738 &lt;in [45] &lt;0.740</td>

<td>0.120 &lt;in [8] &lt;0.122</td><td>0.753 &lt;in [46] &lt;0.755</td>

<td>0.137 &lt;in [9] &lt;0.139</td><td>0.769 &lt;in [47] &lt;0.771</td>

<td>0.154 &lt;in [10] &lt;0.156</td><td>0.784 &lt;in [48] &lt;0.786</td>

<td>0.171 &lt;in [11] &lt;0.173</td><td>0.799 &lt;in [49] &lt;0.801</td>

<td>0.188 &lt;in [12] &lt;0.190</td><td>0.815 &lt;in [50] &lt;0.817</td>

<td>0.205 &lt;in [13] &lt;0.207</td><td>0.830 &lt;in [51] &lt;0.832</td>

<td>0.222 &lt;in [14] &lt;0.229</td><td>0.845 &lt;in [52] &lt;0.847</td>

<td>0.239 &lt;in [15] &lt;0.291</td><td>0.860 &lt;in [53] &lt;0.862</td>

<td>0.256 &lt;in [16] &lt;0.258</td><td>0.874 &lt;in [54] &lt;0.876</td>

<td>0.272 &lt;in [17] &lt;0.274</td><td>0.889 &lt;in [55] &lt;0.891</td>

<td>0.289 &lt;in [18] &lt;0.291</td><td>0.903 &lt;in [56] &lt;0.905</td>

<td>0.306 &lt;in [19] &lt;0.308</td><td>0.917 &lt;in [57] &lt;0.919</td>

<td>0.332 &lt;in [20] &lt;0.325</td><td>0.930 &lt;in [58] &lt;0.932</td>

<td>0.339 &lt;in [21] &lt;0.341</td><td>0.943 &lt;in [59] &lt;0.945</td>

<td>0.356 &lt;in [22] &lt;0.358</td><td>0.956 &lt;in [60] &lt;0.958</td>

<td>0.373 &lt;in [23] &lt;0.375</td><td>0.968 &lt;in [61] &lt;0.970</td>

<td>0.390 &lt;in [24] &lt;0.392</td><td>0.980 &lt;in [62] &lt;0.982</td>

<td>0.407 &lt;in [25] &lt;0.409</td><td>0.992 &lt;in [63] &lt;0.994</td>

<td>0.424 &lt;in [26] &lt;0.426</td><td>1,000 &lt;in [64] &lt;1,002</td>

<td>0.441 &lt;in [27] &lt;0.493</td><td>1,006 &lt;in [65] &lt;1,008</td>

<td>0.458 &lt;in [28] &lt;0.460</td><td>1.012 &lt;in [66] &lt;1.014</td>

<td>0.475 &lt;in [29] &lt;0.477</td><td>1.017 &lt;in [67] &lt;1.019</td>

<td>0.492 &lt;in [30] &lt;0.499</td><td>1.021 &lt;in [68] &lt;1.023</td>

<td>0.509 &lt;in [31] &lt;0.511</td><td>1.026 &lt;in [69] &lt;1.028</td>

<td>0.525 &lt;in [32] &lt;0.527</td><td>1.029 &lt;in [70] &lt;1.031</td>

<td>0.542 &lt;in [33] &lt;0.594</td><td>1.032 &lt;in [71] &lt;1.034</td>

<td>0.559 &lt;in [34] &lt;0.561</td><td>1.035 &lt;in [72] &lt;1.037</td>

<td>0.575 &lt;in [35] &lt;0.577</td><td>1.037 &lt;in [73] &lt;1.039</td>

<td>1.038 &lt;in [74] &lt;1.040</td><td>0.760 &lt;in [112] &lt;0.762</td>

<td>1.039 &lt;in [75] &lt;1.041</td><td>0.745 &lt;in [113] &lt;0.747</td>

115

<td>1.040 &lt;in [76] &lt;1.042</td><td>0.729 &lt;in [114] &lt;0.731</td>

<td>1.040 &lt;in [77] &lt;1.042</td><td>0.713 &lt;in [115] &lt;0.715</td>

<td>1.040 &lt;in [78] &lt;1.042</td><td>0.697 &lt;in [116] &lt;0.699</td>

<td>1.040 &lt;in [79] &lt;1.042</td><td>0.681 &lt;in [117] &lt;0.683</td>

<td>1.039 &lt;in [80] &lt;1.041</td><td>0.664 &lt;in [118] &lt;0.666</td>

<td>1.038 &lt;in [81] &lt;1.040</td><td>0.648 &lt;in [119] &lt;0.650</td>

<td>1.036 &lt;in [82] &lt;1.038</td><td>0.631 &lt;in [120] &lt;0.633</td>

<td>1.034 &lt;in [83] &lt;1.036</td><td>0.614 &lt;in [121] &lt;0.616</td>

<td>1.032 &lt;in [84] &lt;1.034</td><td>0.597 &lt;in [122] &lt;0.599</td>

<td>1.029 &lt;in [85] &lt;1.031</td><td>0.580 &lt;in [123] &lt;0.582</td>

<td>1.025 &lt;in [86] &lt;1.027</td><td>0.563 &lt;in [124] &lt;0.565</td>

<td>1.021 &lt;in [87] &lt;1.023</td><td>0.546 &lt;in [125] &lt;0.548</td>

<td>1.016 &lt;in [88] &lt;1.018</td><td>0.529 &lt;in [126] &lt;0.531</td>

<td>1.011 &lt;in [89] &lt;1.013</td><td>0.512 &lt;in [127] &lt;0.514</td>

<td>1.005 &lt;in [90] &lt;1.007</td><td>-0.497 &lt;in [128] &lt;-0.495</td>

<td>0.999 &lt;in [91] &lt;1.001</td><td>-0.479 &lt;in [129] &lt;-0.477</td>

<td>0.992 &lt;in [92] &lt;0.994</td><td>-0.462 &lt;in [130] &lt;-0.460</td>

<td>0.985 &lt;in [93] &lt;0.987</td><td>-0.445 &lt;in [131] &lt;-0.443</td>

<td>0.977 &lt;in [94] &lt;0.979</td><td>-0.428 &lt;in [132] &lt;-0.426</td>

<td>0.969 &lt;in [95] &lt;0.971</td><td>-0.411 &lt;in [133] &lt;-0.409</td>

<td>0.960 &lt;in [96] &lt;0.962</td><td>-0.394 &lt;in [134] &lt;-0.392</td>

<td>0.951 &lt;in [97] &lt;0.953</td><td>-0.377 &lt;in [135] &lt;-0.375</td>

<td>0.991 &lt;in [98] &lt;0.943</td><td>-0.360 &lt;in [136] &lt;-0.358</td>

<td>0.931 &lt;in [99] &lt;0.933</td><td>-0.343 &lt;in [137] &lt;-0.341</td>

<td>0.920 &lt;in [100] &lt;0.922</td><td>-0.332 &lt;in [138] &lt;-0.325</td>

<td>0.909 &lt;in [101] &lt;0.911</td><td>-0.311 &lt;in [139] &lt;-0.309</td>

<td>0.897 &lt;in [102] &lt;0.899</td><td>-0.295 &lt;in [140] &lt;-0.293</td>

<td>0.885 &lt;in [103] &lt;0.887</td><td>-0.279 &lt;in [141] &lt;-0.277</td>

<td>0.887 &lt;in [104] &lt;0.874</td><td>-0.263 &lt;in [142] &lt;-0.261</td>

<td>0.860 &lt;in [105] &lt;0.862</td><td>-0.248 &lt;in [143] &lt;-0.246</td>

<td>0.846 &lt;in [106] &lt;0.848</td><td>-0.233 &lt;in [144] &lt;-0.231</td>

<td>0.833 &lt;in [107] &lt;0.835</td><td>-0.218 &lt;in [145] &lt;-0.216</td>

<td>0.819 &lt;in [108] &lt;0.821</td><td>-0.203 &lt;in [146] &lt;-0.201</td>

<td>0.804 &lt;in [109] &lt;0.806</td><td>-0.189 &lt;in [147] &lt;-0.187</td>

<td>0.790 &lt;in [110] &lt;0.792</td><td>-0.175 &lt;in [148] &lt;-0.17</td>

116

<td>0.775 &lt;in [111] &lt;0.777</td><td>-0.161 &lt;in [149] &lt;-0.159</td>

<td>-0.147 &lt;in [150] &lt;-0.145</td><td>0.125 &lt;in [188] &lt;0.127</td>

<td>-0.134 &lt;in [151] &lt;-0.132</td><td>0.126 &lt;in [189] &lt;0.128</td>

<td>-0,121 &lt;in [152] &lt;-0,119</td><td>0.126 &lt;in [190] &lt;0.128</td>

<td>-0.108 &lt;in [153] &lt;-0.106</td><td>0.126 &lt;in [191] &lt;0.128</td>

<td>-0.096 &lt;in [154] &lt;-0.094</td><td>0.126 &lt;in [192] &lt;0.128</td>

<td>-0.084 &lt;in [155] &lt;-0.082</td><td>0.127 &lt;in [193] &lt;0.129</td>

<td>-0.072 &lt;in [156] &lt;-0.070</td><td>0.126 &lt;in [194] &lt;0.128</td>

<td>-0.061 &lt;in [157] &lt;-0.059</td><td>0.126 &lt;in [195] &lt;0.128</td>

<td>-0.050 &lt;in [158] &lt;-0.048</td><td>0.125 &lt;in [196] &lt;0.127</td>

<td>-0.039 &lt;in [159] &lt;-0.037</td><td>0.124 &lt;in [197] &lt;0.126</td>

<td>-0.028 &lt;in [160] &lt;-0.026</td><td>0.123 &lt;in [198] &lt;0.125</td>

<td>-0.018 &lt;in [161] &lt;-0.016</td><td>0.122 &lt;in [199] &lt;0.124</td>

<td>-0.008 &lt;in [162] &lt;-0.006</td><td>0.121 &lt;in [200] &lt;0.123</td>

<td>0.001 &lt;in [163] &lt;0.003</td><td>0.119 &lt;in [201] &lt;0.121</td>

<td>0.010 &lt;in [164] &lt;0.012</td><td>0.118 &lt;in [202] &lt;0.120</td>

<td>0.019 &lt;in [165] &lt;0.021</td><td>0.116 &lt;in [203] &lt;0.118</td>

<td>0.028 &lt;in [166] &lt;0.030</td><td>0.114 &lt;in [204] &lt;0.116</td>

<td>0.036 &lt;in [167] &lt;0.038</td><td>0.111 &lt;in [205] &lt;0.113</td>

<td>0.043 &lt;in [168] &lt;0.045</td><td>0.109 &lt;in [206] &lt;0.111</td>

<td>0.051 &lt;in [169] &lt;0.053</td><td>0.107 &lt;in [207] &lt;0.109</td>

<td>0.058 &lt;in [170] &lt;0.060</td><td>0.104 &lt;in [208] &lt;0.106</td>

<td>0.065 &lt;in [171] &lt;0.067</td><td>0.102 &lt;in [209] &lt;0.104</td>

<td>0.071 &lt;in [172] &lt;0.073</td><td>0.099 &lt;in [210] &lt;0.101</td>

<td>0.077 &lt;in [173] &lt;0.079</td><td>0.096 &lt;in [211] &lt;0.098</td>

<td>0.082 &lt;in [179] &lt;0.084</td><td>0.093 &lt;in [212] &lt;0.095</td>

<td>0.088 &lt;in [175] &lt;0.090</td><td>0.090 &lt;in [213] &lt;0.092</td>

<td>0.093 &lt;in [176] &lt;0.095</td><td>0.087 &lt;in [214] &lt;0.089</td>

<td>0.097 &lt;in [177] &lt;0.099</td><td>0.084 &lt;in [215] &lt;0.086</td>

<td>0.101 &lt;in [178] &lt;0.103</td><td>0.082 &lt;in [216] &lt;0.084</td>

<td>0.105 &lt;in [179] &lt;0.107</td><td>0.079 &lt;in [217] &lt;0.081</td>

<td>0.109 &lt;in [180] &lt;0.111</td><td>0.076 &lt;in [218] &lt;0.078</td>

<td>0.112 &lt;in [181] &lt;0.114</td><td>0.073 &lt;in [219] &lt;0.075</td>

<td>0.115 &lt;in [182] &lt;0.117</td><td>0.070 &lt;in [220] &lt;0.072</td>

<td>0.117 &lt;in [183] ​​&lt;0.119</td><td>0.067 &lt;in [221] &lt;0.069</td>

117

<td>0.119 &lt;in [184] &lt;0.121</td><td>0.069 &lt;in [222] &lt;0.066</td>

<td>0.121 &lt;in [185] &lt;0.123</td><td>0.061 &lt;in [223] &lt;0.063</td>

<td>0.123 &lt;in [186] &lt;0.125</td><td>0.058 &lt;in [224] &lt;0.060</td>

<td>0.124 &lt;in [187] &lt;0.126</td><td>0.055 &lt;in [225] &lt;0.057</td>

<td>0.053 &lt;in [226] &lt;0.055</td><td>-0.006 &lt;in [264] &lt;-0.004</td>

<td>0.050 &lt;in [227] &lt;0.052</td><td>-0.006 &lt;in [265] &lt;-0.004</td>

<td>0.047 &lt;in [228] &lt;0.049</td><td>-0.005 &lt;in [266] &lt;-0.003</td>

<td>0.045 &lt;in [229] &lt;0.047</td><td>-0.005 &lt;in [267] &lt;-0.003</td>

<td>0.043 &lt;in [230] &lt;0.045</td><td>-0.005 &lt;in [268] &lt;-0.003</td>

<td>0.040 &lt;in [231] &lt;0.042</td><td>-0.005 &lt;in [269] &lt;-0.003</td>

<td>0.038 &lt;in [232] &lt;0.040</td><td>-0.004 &lt;in [270] &lt;-0.002</td>

<td>0.036 &lt;in [233] &lt;0.038</td><td>-0.004 &lt;in [271] &lt;-0.002</td>

<td>0.034 &lt;in [234] &lt;0.036</td><td>-0.004 &lt;in [272] &lt;-0.002</td>

<td>0.032 &lt;in [235] &lt;0.034</td><td>-0.003 &lt;in [273] &lt;-0.001</td>

<td>0.030 &lt;in [236] &lt;0.032</td><td>-0.003 &lt;in [279] &lt;-0.001</td>

<td>0.028 &lt;in [237] &lt;0.030</td><td>-0.003 &lt;in [275] &lt;-0.001</td>

<td>0.027 &lt;in [238] &lt;0.029</td><td>-0.003 &lt;in [276] &lt;-0.001</td>

<td>0.025 &lt;in [239] &lt;0.027</td><td>-0.002 &lt;in [277] &lt;0.000</td>

<td>0.023 &lt;in [240] &lt;0.025</td><td>-0.002 &lt;in [278] &lt;0.000</td>

<td>0.022 &lt;in [241] &lt;0.024</td><td>-0.002 &lt;in [279] &lt;0.000</td>

<td>0.021 &lt;in [242] &lt;0.023</td><td>-0.002 &lt;in [280] &lt;0.000</td>

<td>0.019 &lt;in [243] &lt;0.021</td><td>-0.002 &lt;in [281] &lt;0.000</td>

<td>0.018 &lt;in [294] &lt;0.020</td><td>-0.002 &lt;in [282] &lt;0.000</td>

<td>0.017 &lt;in [245] &lt;0.019</td><td>-0.001 &lt;in [283] &lt;0.001</td>

<td>0.016 &lt;in [246] &lt;0.018</td><td>-0.001 &lt;in [284] &lt;0.001</td>

<td>0.015 &lt;in [297] &lt;0.017</td><td>-0.001 &lt;in [285] &lt;0.001</td>

<td>0.014 &lt;in [248] &lt;0.016</td><td>-0.001 &lt;in [286] &lt;0.001</td>

<td>0.013 &lt;in [249] &lt;0.015</td><td>0.000 &lt;in [287] &lt;0.002</td>

<td>0.012 &lt;in [250] &lt;0.014</td><td>0.000 &lt;in [288] &lt;0.002</td>

<td>0.011 &lt;in [251] &lt;0.013</td><td>0.000 &lt;in [289] &lt;0.002</td>

<td>0.010 &lt;in [252] &lt;0.012</td><td>0.000 &lt;in [290] &lt;0.002</td>

<td>0.009 &lt;in [253] &lt;0.011</td><td>0.000 &lt;in [291] &lt;0.002</td>

<td>0.009 &lt;in [254] &lt;0.011</td><td>0.001 &lt;in [292] &lt;0.003</td>

<td>0.008 &lt;in [255] &lt;0.010</td><td>0.001 &lt;in [293] &lt;0.003</td>

<td>-0.009 &lt;in [256] &lt;-0.007</td><td>0.001 &lt;in [294] &lt;0.003</td>

118

<td>-0.009 &lt;in [257] &lt;-0.007</td><td>0.001 &lt;in [295] &lt;0.003</td>

<td>-0.008 &lt;in [258] &lt;-0.006</td><td>0.000 &lt;in [296] &lt;0.002</td>

<td>-0.008 &lt;in [259] &lt;-0.006</td><td>0.000 &lt;in [297] &lt;0.002</td>

<td>-0.008 &lt;in [260] &lt;-0.006</td><td>0.000 &lt;in [298] &lt;0.002</td>

<td>-0.007 &lt;in [261] &lt;-0.005</td><td>-0.001 &lt;in [299] &lt;0.001</td>

<td>-0.007 &lt;in [262] &lt;-0.005</td><td>-0.001 &lt;in [300] &lt;0.001</td>

<td>-0.006 &lt;in [263] &lt;-0.004</td><td>-0.002 &lt;in [301] &lt;0.000</td>

<td>-0.002 &lt;in [302] &lt;0.000</td><td>0.000 &lt;in [340] &lt;0.002</td>

<td>-0.003 &lt;in [303] &lt;-0.001</td><td>0.000 &lt;in [391] &lt;0.002</td>

<td>-0.003 &lt;in [304] &lt;-0.001</td><td>0.000 &lt;in [392] &lt;0.002</td>

<td>-0.004 &lt;in [305] &lt;-0.002</td><td>0.000 &lt;in [393] &lt;0.002</td>

<td>-0.004 &lt;in [306] &lt;-0.002</td><td>-0.001 &lt;in [344] &lt;0.001</td>

<td>-0.004 &lt;in [307] &lt;-0.002</td><td>-0.001 &lt;in [345] &lt;0.001</td>

<td>-0.005 &lt;in [308] &lt;-0.003</td><td>0.000 &lt;in [396] &lt;0.002</td>

<td>-0.005 &lt;in [309] &lt;-0.003</td><td>0.000 &lt;in [347] &lt;0.002</td>

<td>-0.005 &lt;in [310] &lt;-0.003</td><td>0.001 &lt;in [348] &lt;0.003</td>

<td>-0.006 &lt;in [311] &lt;-0.004</td><td>0.001 &lt;in [399] &lt;0.003</td>

<td>-0.006 &lt;in [312] &lt;-0.004</td><td>0.001 &lt;in [350] &lt;0.003</td>

<td>-0.006 &lt;in [313] &lt;-0.004</td><td>0.002 &lt;in [351] &lt;0.004</td>

<td>-0.006 &lt;in [314] &lt;-0.004</td><td>0.002 &lt;in [352] &lt;0.004</td>

<td>-0.006 &lt;in [315] &lt;-0.004</td><td>0.002 &lt;in [353] &lt;0.004</td>

<td>-0.006 &lt;in [316] &lt;-0.004</td><td>0.002 &lt;in [354] &lt;0.004</td>

<td>-0.005 &lt;in [317] &lt;-0.003</td><td>0.002 &lt;in [355] &lt;0.004</td>

<td>-0.005 &lt;in [318] &lt;-0.003</td><td>0.001 &lt;in [356] &lt;0.003</td>

<td>-0.005 &lt;in [319] &lt;-0.003</td><td>0.001 &lt;in [357] &lt;0.003</td>

<td>-0.005 &lt;in [320] &lt;-0.003</td><td>0.001 &lt;in [358] &lt;0.003</td>

<td>-0.004 &lt;in [321] &lt;-0.002</td><td>0.001 &lt;in [359] &lt;0.003</td>

<td>-0.004 &lt;in [322] &lt;-0.002</td><td>0.001 &lt;in [360] &lt;0.003</td>

<td>-0.004 &lt;in [323] &lt;-0.002</td><td>0.000 &lt;in [361] &lt;0.002</td>

<td>-0.003 &lt;in [324] &lt;-0.001</td><td>0.000 &lt;in [362] &lt;0.002</td>

<td>-0.003 &lt;in [325] &lt;-0.001</td><td>0.000, &lt;in [363] &lt;0.002</td>

<td>-0.003 &lt;in [326] &lt;-0.001</td><td>-0.001 &lt;in [364] &lt;0.001</td>

<td>-0.002 &lt;in [327] &lt;0.000</td><td>-0.001 &lt;in [365] &lt;0.001</td>

<td>-0.002 &lt;in [328] &lt;0.000</td><td>-0.001 &lt;in [366] &lt;0.001</td>

<td>-0.001 &lt;in [329] &lt;0.001</td><td>-0.001 &lt;in [367] &lt;0.001</td>

119

<td>-0.001 &lt;in [330] &lt;0.001</td><td>-0.002 &lt;in [368] &lt;0.000</td>

<td>-0.001 &lt;in [331] &lt;0.001</td><td>-0.002 &lt;in [369] &lt;0.000</td>

<td>-0.001 &lt;in [332] &lt;0.001</td><td>-0.002 &lt;in [370] &lt;0.000</td>

<td>-0.001 &lt;in [333] &lt;0.001</td><td>-0.002 &lt;in [371] &lt;0.000</td>

<td>0.000 &lt;in [334] &lt;0.002</td><td>-0.002 &lt;in [372] &lt;0.000</td>

<td>0.000 &lt;in [335] &lt;0.002</td><td>-0.002 &lt;in [373] &lt;0.000</td>

<td>0.000 &lt;in [336] &lt;0.002</td><td>-0.002 &lt;in [379] &lt;0.000</td>

<td>0.000 &lt;in [337] &lt;0.002</td><td>-0.002 &lt;in [375] &lt;0.000</td>

<td>0.000 &lt;in [338] &lt;0.002</td><td>-0.002 &lt;in [376] &lt;0.000</td>

<td>0.000 &lt;in [339] &lt;0.002</td><td>-0.002 &lt;in [377] &lt;0.000</td>

<td>-0.002 &lt;in [378] &lt;0.000</td><td>-0.001 &lt;in [416] &lt;0.001</td>

<td>-0.002 &lt;in [379] &lt;0.000</td><td>-0.001 &lt;in [417] &lt;0.001</td>

<td>-0.002 &lt;in [380] &lt;0.000</td><td>-0.001 &lt;in [418] &lt;0.001</td>

<td>-0.002 &lt;in [381] &lt;0.000</td><td>-0.001 &lt;in [419] &lt;0.001</td>

<td>-0.002 &lt;in [382] &lt;0.000</td><td>-0.001 &lt;in [420] &lt;0.001</td>

<td>-0.002 &lt;in [383] &lt;0.000</td><td>-0.001 &lt;in [421] &lt;0.001</td>

<td>0.000 &lt;in [384] &lt;0.002</td><td>-0.001 &lt;in [422] &lt;0.001</td>

<td>0.000 &lt;in [385] &lt;0.002</td><td>-0.001 &lt;in [423] &lt;0.001</td>

<td>0.000 &lt;in [386] &lt;0.002</td><td>-0.001 &lt;in [424] &lt;0.001</td>

<td>0.000 &lt;in [387] &lt;0.002</td><td>-0.001 &lt;in [425] &lt;0.001</td>

<td>0.000 &lt;in [388] &lt;0.002</td><td>-0.001 &lt;in [426] &lt;0.001</td>

<td>0.000 &lt;in [389] &lt;0.002</td><td>-0.001 &lt;in [427] &lt;0.001</td>

<td>0.000 &lt;in [390] &lt;0.002</td><td>-0.001 &lt;in [428] &lt;0.001</td>

<td>0.000 &lt;in [391] &lt;0.002</td><td>-0.001 &lt;in [429] &lt;0.001</td>

<td>0.000 &lt;in [392] &lt;0.002</td><td>-0.001 &lt;in [430] &lt;0.001</td>

<td>0.000 &lt;in [393] &lt;0.002</td><td>-0.001 &lt;in [431] &lt;0.001</td>

<td>-0.001 &lt;in [394] &lt;0.001</td><td>-0.001 &lt;in [432] &lt;0.001</td>

<td>-0.001 &lt;in [395] &lt;0.001</td><td>-0.001 &lt;in [433] &lt;0.001</td>

<td>-0.001 &lt;in [396] &lt;0.001</td><td>-0.001 &lt;in [434] &lt;0.001</td>

<td>-0.001 &lt;in [397] &lt;0.001</td><td>-0.001 &lt;in [435] &lt;0.001</td>

<td>-0.001 &lt;in [398] &lt;0.001</td><td>-0.001 &lt;in [436] &lt;0.001</td>

<td>-0.001 &lt;in [399] &lt;0.001</td><td>-0.001 &lt;in [437] &lt;0.001</td>

<td>-0.001 &lt;in [400] &lt;0.001</td><td>-0.001 &lt;in [438] &lt;0.001</td>

<td>-0.001 &lt;in [401] &lt;0.001</td><td>-0.001 &lt;in [439] &lt;0.001</td>

<td>-0.001 &lt;in [402] &lt;0.001</td><td>-0.001 &lt;in [440] &lt;0.001</td>

120

<td>-0.001 &lt;in [403] &lt;0.001</td><td>-0.001 &lt;in [441] &lt;0.001-</td>

<td>-0.001 &lt;in [409] &lt;0.001</td><td>-0.001 &lt;in [442] &lt;0.001</td>

<td>-0.001 &lt;in [405] &lt;0.001</td><td>-0.001 &lt;in [443] &lt;0.001</td>

<td>-0.001 &lt;in [406] &lt;0.001</td><td>-0.001 &lt;in [444] &lt;0.001</td>

<td>-0.001 &lt;in [407] &lt;0.001</td><td>-0.001 &lt;in [445] &lt;0.001</td>

<td>-0.001 &lt;in [408] &lt;0.001</td><td>-0.001 &lt;in [446] &lt;0.001</td>

<td>-0.001 &lt;in [409] &lt;0.001</td><td>-0.001 &lt;in [447] &lt;0.001</td>

<td>-0.001 &lt;in [410] &lt;0.001</td><td>-0.001 &lt;in [448] &lt;0.001</td>

<td>-0.001 &lt;in [411] &lt;0.001</td><td>-0.001 &lt;in [449] &lt;0.001</td>

<td>-0.001 &lt;in [412] &lt;0.001</td><td>-0.001 &lt;in [450] &lt;0.001</td>

<td>-0.001 &lt;in [413] &lt;0.001</td><td>-0.001 &lt;in [451] &lt;0.001</td>

<td>-0.001 &lt;in [414] &lt;0.001</td><td>-0.001 &lt;in [452] &lt;0.001</td>

<td>-0.001 &lt;in [415] &lt;0.001</td><td>-0.001 &lt;in [453] &lt;0.001</td>

<td>-0.001 &lt;in [454] &lt;0.001</td><td>-0.001 &lt;in [492] &lt;0.001</td>

<td>-0.001 &lt;in [455] &lt;0.001</td><td>-0.001 &lt;in [493] &lt;0.001</td>

<td>-0.001 &lt;in [456] &lt;0.001</td><td>-0.001 &lt;in [494] &lt;0.001</td>

<td>-0.001 &lt;in [457] &lt;0.001</td><td>-0.001 &lt;in [495] &lt;0.001</td>

<td>-0.001 &lt;in [458] &lt;0.001</td><td>-0.001 &lt;in [496] &lt;0.001</td>

<td>0.001 &lt;in [459] &lt;0.001</td><td>-0.001 &lt;in [497] &lt;0.001</td>

<td>-0.001 &lt;in [460] &lt;0.001</td><td>-0.001 &lt;in [498] &lt;0.001</td>

<td>-0.001 &lt;in [461] &lt;0.001</td><td>-0.001 &lt;in [499] &lt;0.001</td>

<td>-0.001 &lt;in [462] &lt;0.001</td><td>-0.001 &lt;in [500] &lt;0.001</td>

<td>-0.001 &lt;in [463] &lt;0.001</td><td>-0.001 &lt;in [501] &lt;0.001</td>

<td>-0.001 &lt;in [464] &lt;0.001</td><td>-0.001 &lt;in [502] &lt;0.001</td>

<td>-0.001 &lt;in [465] &lt;0.001</td><td>-0.001 &lt;in [503] &lt;0.001</td>

<td>-0.001 &lt;in [466] &lt;0.001</td><td>-0.001 &lt;in [504] &lt;0.001</td>

<td>-0.001 &lt;in [467] &lt;0.001</td><td>-0.001 &lt;in [505] &lt;0.001</td>

<td>-0.001 &lt;in [468] &lt;0.001</td><td>-0.001 &lt;in [506] &lt;0.001</td>

<td>-0.001 &lt;in [469] &lt;0.001</td><td>-0.001 &lt;in [507] &lt;0.001</td>

<td>-0.001 &lt;in [470] &lt;0.001</td><td>-0.001 &lt;in [508] &lt;0.001</td>

<td>-0.001 &lt;in [471] &lt;0.001</td><td>-0.001 &lt;in [509] &lt;0.001</td>

<td>-0.001 &lt;in [472] &lt;0.001</td><td>-0.001 &lt;in [510] &lt;0.001</td>

<td>-0.001 &lt;in [473] &lt;0.001</td><td>-0.001 &lt;in [511] &lt;0.001</td>

<td>-0.001 &lt;in [474] &lt;0.001</td><td>-0.001 &lt;in [512] &lt;0.001</td>

<td>-0.001 &lt;in [475] &lt;0.001</td><td>-0.001 &lt;in [513] &lt;0.001</td>

121

<td>-0.001 &lt;in [476] &lt;0.001</td><td>-0.001 &lt;in [514] &lt;0.001</td>

<td>-0.001 &lt;in [477] &lt;0.001</td><td>-0.001 &lt;in [515] &lt;0.001</td>

<td>-0.001 &lt;in [478] &lt;0.001</td><td>-0.001 &lt;in [516] &lt;0.001</td>

<td>0.000 &lt;in [479] &lt;0.002</td><td>-0.001 &lt;in [517] &lt;0.001</td>

<td>-0.001 &lt;in [480] &lt;0.001</td><td>-0.001 &lt;in [518] &lt;0.001</td>

<td>-0.001 &lt;in [481] &lt;0.001</td><td>-0.001 &lt;in [519] &lt;0.001</td>

<td>-0.001 &lt;in [482] &lt;0.001</td><td>-0.001 &lt;in [520] &lt;0.001</td>

<td>-0.001 &lt;in [483] &lt;0.001</td><td>-0.001 &lt;in [521] &lt;0.001</td>

<td>-0.001 &lt;in [484] &lt;0.001</td><td>-0.001 &lt;in [522] &lt;0.001</td>

<td>-0.001 &lt;in [485] &lt;0.001</td><td>-0.001 &lt;in [523] &lt;0.001</td>

<td>-0.001 &lt;in [486] &lt;0.001</td><td>-0.001 &lt;in [529] &lt;0.001</td>

<td>-0.001 &lt;in [487] &lt;0.001</td><td>-0.001 &lt;in [525] &lt;0.001</td>

<td>-0.001 &lt;in [488] &lt;0.001</td><td>-0.001 &lt;in [526] &lt;0.001</td>

<td>-0.001 &lt;in [489] &lt;0.001</td><td>-0.001 &lt;in [527] &lt;0.001</td>

<td>-0.001 &lt;in [490] &lt;0.001</td><td>-0.001 &lt;in [528] &lt;0.001</td>

<td>-0.001 &lt;in [491] &lt;0.001</td><td>-0.001 &lt;in [529] &lt;0.001</td>

<td>-0.001 &lt;in [530] &lt;0.001</td><td>-0.001 &lt;in [568] &lt;0.001</td>

<td>-0.001 &lt;in [531] &lt;0.001</td><td>-0.001 &lt;in [569] &lt;0.001</td>

<td>-0.001 &lt;in [532] &lt;0.001</td><td>-0.001 &lt;in [570] &lt;0.001</td>

<td>-0.001 &lt;in [533] &lt;0.001</td><td>-0.001 &lt;in [571] &lt;0.001</td>

<td>-0.001 &lt;in [534] &lt;0.001</td><td>-0.001 &lt;in [572] &lt;0.001</td>

<td>-0.001 &lt;in [535] &lt;0.001</td><td>-0.001 &lt;in [573] &lt;0.001</td>

<td>-0.001 &lt;in [536] &lt;0.001</td><td>-0.001 &lt;in [574] &lt;0.001</td>

<td>-0.001 &lt;in [537] &lt;0.001</td><td>-0.001 &lt;in [575] &lt;0.001</td>

<td>-0.001 &lt;in [538] &lt;0.001</td><td>-0.001 &lt;in [576] &lt;0.001</td>

<td>-0.001 &lt;in [539] &lt;0.001</td><td>-0.001 &lt;in [577] &lt;0.001</td>

<td>-0.001 &lt;in [540] &lt;0.001</td><td>-0.001 &lt;in [578] &lt;0.001</td>

<td>-0.001 &lt;in [541] &lt;0.001</td><td>-0.001 &lt;in [579] &lt;0.001</td>

<td>-0.001 &lt;in [542] &lt;0.001</td><td>-0.001 &lt;in [580] &lt;0.001</td>

<td>-0.001 &lt;in [543] &lt;0.001</td><td>-0.001 &lt;in [581] &lt;0.001</td>

<td>-0.001 &lt;in [544] &lt;0.001</td><td>-0.001 &lt;in [582] &lt;0.001</td>

<td>-0.001 &lt;in [545] &lt;0.001</td><td>-0.001 &lt;in [583] &lt;0.001</td>

<td>-0.001 &lt;in [546] &lt;0.001</td><td>-0.001 &lt;in [584] &lt;0.001</td>

<td>-0.001 &lt;in [547] &lt;0.001</td><td>-0.001 &lt;in [585] &lt;0.001</td>

<td>-0.001 &lt;in [548] &lt;0.001</td><td>-0.001 &lt;in [586] &lt;0.001</td>

122

<td>-0.001 &lt;in [549] &lt;0.001</td><td>-0.001 &lt;in [587] &lt;0.001</td>

<td>-0.001 &lt;in [550] &lt;0.001</td><td>-0.001 &lt;in [588] &lt;0.001</td>

<td>-0.001 &lt;in [551] &lt;0.001</td><td>-0.001 &lt;in [589] &lt;0.001</td>

<td>-0.001 &lt;in [552] &lt;0.001</td><td>-0.001 &lt;in [590] &lt;0.001</td>

<td>-0.001 &lt;in [553] &lt;0.001</td><td>-0.001 &lt;in [591] &lt;0.001</td>

<td>-0.001 &lt;in [554] &lt;0.001</td><td>-0.001 &lt;in [592] &lt;0.001</td>

<td>-0.001 &lt;in [555] &lt;0.001</td><td>-0.001 &lt;in [593] &lt;0.001</td>

<td>-0.001 &lt;in [556] &lt;0.001</td><td>-0.001 &lt;in [594] &lt;0.001</td>

<td>-0.001 &lt;in [557] &lt;0.001</td><td>-0.001 &lt;in [595] &lt;0.001</td>

<td>-0.001 &lt;in [558] &lt;0.001</td><td>-0.001 &lt;in [596] &lt;0.001</td>

<td>-0.001 &lt;in [559] &lt;0.001</td><td>-0.001 &lt;in [597] &lt;0.001</td>

<td>-0.001 &lt;in [560] &lt;0.001</td><td>-0.001 &lt;in [598] &lt;0.001</td>

<td>-0.001 &lt;in [561] &lt;0.001</td><td>-0.001 &lt;in [599] &lt;0.001</td>

<td>-0.001 &lt;in [562] &lt;0.001</td><td>-0.001 &lt;in [600] &lt;0.001</td>

<td>-0.001 &lt;in [563] &lt;0.001</td><td>-0.001 &lt;in [601] &lt;0.001</td>

<td>-0.001 &lt;in [564] &lt;0.001</td><td>-0.001 &lt;in [602] &lt;0.001</td>

<td>-0.001 &lt;in [565] &lt;0.001</td><td>-0.001 &lt;in [603] &lt;0.001</td>

<td>-0.001 &lt;in [566] &lt;0.001</td><td>-0.001 &lt;in [604] &lt;0.001</td>

<td>-0.001 &lt;in [567] &lt;0.001 -0.001 &lt;in [606] &lt;0.001 -0.001 &lt;in [607] &lt;0.001 -0.001 &lt;in [608] &lt;0.001 -0.001 &lt;in [609] &lt;0.001 -0.001 &lt;in [ 610] &lt;0.001 -0.001 &lt;in [611] &lt;0.001 -0.001 &lt;in [612] &lt;0.001 -0.001 &lt;in [613] &lt;0.001 -0.001 &lt;in [614] &lt;0.001 -0.001 &lt;in [615] &lt;0.001 - 0.001 &lt;in [616] &lt;0.001 -0.001 &lt;in [617] &lt;0.001 -0.001 &lt;in [618] &lt;0.001 -0.001 &lt;in [619] &lt;0.001 -0.001 &lt;in [620] &lt;0.001 -0.001 &lt;in [621 ] &lt;0.001</td><td>-0.001 &lt;in [605] &lt;0.001</td>

123

-0.001 &lt;in [622] &lt;0.001 -0.001 &lt;in [623] &lt;0.001 -0.001 &lt;in [624] &lt;0.001 -0.001 &lt;in [625] &lt;0.001 -0.001 &lt;in [626] &lt;0.001 -0.001 &lt;in [ 627] &lt;0.001 -0.001 &lt;in [628] &lt;0.001 -0.001 &lt;in [629] &lt;0.001 -0.001 &lt;in [630] &lt;0.001 -0.001 &lt;in [631] &lt;0.001 -0.001 &lt;in [632] &lt;0.001 - 0.001 &lt;in [633] &lt;0.001 -0.001 &lt;in [634] &lt;0.001 -0.001 &lt;in [635] &lt;0.001 -0.001 &lt;in [636] &lt;0.001 -0.001 &lt;in [637] &lt;0.001 -0.001 &lt;in [638 ] &lt;0.001 -0.001 &lt;in [639] &lt;0.001

Annex 4 [362]

0,010 &lt; 0,023 &lt; 0,034 &lt; 0,045 &lt; 0,058 &lt; 0,072 &lt; 0,087 &lt; 0,103 &lt; 0,120 &lt; 0,137 &lt; 0,154 &lt;

in [0] &lt;0.012 in [1] | &lt;0.025 in [2] | &lt;0.036 in [3] | &lt;0.097 in [4] | &lt;0.060 in [5] | &lt;0.074 in [6] | &lt;0.089 in [7] | &lt;0.105 in [8] | &lt;0.122 in [9] | &lt;0.139 in [10] | &lt;0.156

0,592 &lt; 0,609 &lt; 0,625 &lt; 0,642 &lt; 0,658 &lt; 0,674 &lt; 0,690 &lt; 0,706 &lt; 0,722 &lt; 0,738 &lt; 0,753 &lt; 0,769 &lt; 0,784 &lt;

in [36] in [37] in [38] in [39] in [40] in [91] in [42] in [93] in [44] in [45] in [46] in [47] in [ 48] &lt;0.594 &lt;0.611 &lt;0.627 &lt;0.644 &lt;0.660 &lt;0.676 &lt;0.692 &lt;0.708 &lt;0.724 &lt;0.740 &lt;0.755 &lt;0.771 &lt;0.786

124

<td> 0,171 &lt;</td><td>in [11]</td><td> &lt; 0,173</td><td> 0,799 &lt;</td><td>in [49] |</td>

<td> 0,188 &lt;</td><td>in [12]</td><td> &lt; 0,190</td><td> 0,815 &lt;</td><td>in [50]</td>

<td> 0,205 &lt;</td><td>in [13]</td><td> &lt; 0,207</td><td> 0,830 &lt;</td><td>in [51]</td>

<td> 0,222 &lt;</td><td>in [14]</td><td> &lt; 0,229</td><td> 0,845 &lt;</td><td>in [52] |</td>

<td> 0,239 &lt;</td><td>in [15]</td><td> &lt; 0,241</td><td> 0,860 &lt;</td><td>in [53]</td>

<td> 0,256 &lt;</td><td>in [16]</td><td> &lt; 0,258</td><td> 0,874 &lt;</td><td>in [54] |</td>

<td> 0,272 &lt;</td><td>in [17]</td><td> &lt; 0,274</td><td> 0,889 &lt;</td><td>in [55] |</td>

<td> 0,289 &lt;</td><td>in [18]</td><td> &lt; 0,291</td><td> 0,903 &lt;</td><td>in [56]</td>

<td> 0,306 &lt;</td><td>in [19]</td><td> &lt; 0,308</td><td> 0,917 &lt;</td><td>in [57] |</td>

<td> 0,323 &lt;</td><td>in [20]</td><td> &lt; 0,325</td><td> 0,930 &lt;</td><td>in [58]</td>

<td> 0,339 &lt;</td><td>in [21]</td><td> &lt; 0,341</td><td> 0,943 &lt;</td><td>in [59]</td>

<td> 0,356 &lt;</td><td>in [22]</td><td> &lt; 0,358</td><td> 0,956 &lt;</td><td>in [60] |</td>

<td> 0,373 &lt;</td><td>in [23]</td><td> &lt;0,375</td><td> 0,968 &lt;</td><td>in [61]</td>

<td> 0,390 &lt;</td><td>in [24]</td><td> &lt; 0,392</td><td> 0,980 &lt;</td><td>in [62]</td>

<td> 0,407 &lt;</td><td>in [25]</td><td> &lt; 0,909</td><td> 0,992 &lt;</td><td>in [63]</td>

<td> 0,424 &lt;</td><td>in [26]</td><td> &lt; 0,426</td><td> 1,000 &lt;</td><td>in [64]</td>

<td> 0,441 &lt;</td><td>in [27]</td><td> &lt; 0,493</td><td> 1,006 &lt;</td><td>in [65]</td>

<td> 0,958 &lt;</td><td>in [28]</td><td> &lt; 0,960</td><td> 1,012 &lt;</td><td>in [66]</td>

<td> 0,975 &lt;</td><td>in [29]</td><td> &lt; 0,977</td><td> 1,017 &lt;</td><td>in [67] |</td>

<td> 0,492 &lt;</td><td>in [30]</td><td> &lt; 0,499</td><td> 1,021 &lt;</td><td>in [68]</td>

<td> 0,509 &lt;</td><td>in [31]</td><td> &lt; 0,511</td><td> 1,026 &lt;</td><td>in [69]</td>

<td> 0,525 &lt;</td><td>in [32]</td><td> &lt; 0,527</td><td> 1,029 &lt;</td><td>in [70] |</td>

<td> 0,542 &lt;</td><td>in [33]</td><td> &lt; 0,599</td><td> 1,032 &lt;</td><td>in [71]</td>

<td> 0,559 &lt;</td><td>in [34]</td><td> &lt; 0,561</td><td> 1,035 &lt;</td><td>in [72] |</td>

<td> 0,575 &lt;</td><td>in [35]</td><td> &lt; 0,577</td><td> 1,037 &lt;</td><td>in [73]</td>

<td> 1,038 &lt;</td><td>in [74]</td><td> &lt; 1,040</td><td> 0,760 &lt;</td><td>in [112]</td>

<td> 1,039 &lt;</td><td>in [75]</td><td> &lt; 1,091</td><td> 0,745 &lt;</td><td>in [113]</td>

<td> 1,040 &lt;</td><td>in [76]</td><td> &lt; 1,042</td><td> 0,729 &lt;</td><td>in [114]</td>

<td> 1,040 &lt;</td><td>in [77]</td><td> &lt; 1,042</td><td> 0,713 &lt;</td><td>in [115]</td>

<td> 1,040 &lt;</td><td>in [78]</td><td> &lt; 1,042</td><td> 0,697 &lt;</td><td>in [116]</td>

<td> 1,040 &lt;</td><td>in [79]</td><td> &lt; 1,042</td><td> 0,681 &lt;</td><td>in [117]</td>

<td> 1,039 &lt;</td><td>in [80]</td><td> &lt;1,041</td><td> 0,664 &lt;</td><td>in [118]</td>

<td> 1,038 &lt;</td><td>in [81]</td><td> &lt; 1,040</td><td> 0,648 &lt;</td><td>in [119]</td>

<td> 1,036 &lt;</td><td>in [82]</td><td> &lt; 1,038</td><td> 0,631 &lt;</td><td>in [120]</td>

<td> 1,034 &lt;</td><td>in [83]</td><td> &lt; 1,036</td><td> 0,614 &lt;</td><td>in [121]</td>

&lt; 0,801 &lt; 0,817 &lt; 0,832 &lt; 0,847 &lt; 0,862 &lt; 0,876 &lt; 0,891 &lt; 0,905 &lt; 0,919 &lt; 0,932 &lt; 0,945 &lt; 0,958 &lt; 0,970 &lt; 0,982 &lt; 0,994 &lt; 1,002 &lt; 1,008 &lt; 1,014 &lt; 1,019 &lt; 1,023 &lt; 1,028 &lt; 1,031 &lt; 1,034 &lt; 1,037 &lt; 1,039 | &lt; 0,762 | &lt; 0,747 | &lt; 0,731 | &lt; 0,715 | &lt; 0,699 | &lt; 0,683 | &lt; 0,666 | &lt; 0,650 | &lt; 0,633 | &lt; 0,616

125

<td> 1,032 &lt;</td><td>in [89]</td><td> &lt; 1,034</td><td> 0,597 &lt;</td><td>in [122]</td><td> &lt; 0,599</td>

<td> 1,029 &lt;</td><td>in [85]</td><td> &lt; 1,031</td><td> 0,580 &lt;</td><td>in [123]</td><td> &lt; 0,582</td>

<td> 1,025 &lt;</td><td>in [86]</td><td> &lt; 1,027</td><td> 0,563 &lt;</td><td>in [124]</td><td> &lt; 0,565</td>

<td> 1,021 &lt;</td><td>in [87]</td><td> &lt; 1,023</td><td> 0,546 &lt;</td><td>in [125]</td><td> &lt; 0,548</td>

<td> 1,016 &lt;</td><td>in [88]</td><td> &lt; 1,018</td><td> 0,529 &lt;</td><td>in [126]</td><td> &lt; 0,531</td>

<td> 1,011 &lt;</td><td>in [89]</td><td> &lt; 1,013</td><td> 0,512 &lt;</td><td>in [127]</td><td> &lt; 0,514</td>

<td> 1,005 &lt;</td><td>in [90]</td><td> &lt; 1,007</td><td> 0,495 &lt;</td><td>in [128]</td><td> &lt; 0,497</td>

<td> 0,999 &lt;</td><td>in [91]</td><td> &lt; 1,001</td><td> 0,477 &lt;</td><td>in [129]</td><td> &lt; 0,479</td>

<td> 0,992 &lt;</td><td>in [92]</td><td> &lt; 0,999</td><td> 0,460 &lt;</td><td>in [130]</td><td> &lt; 0,462</td>

<td> 0,985 &lt;</td><td>in [93]</td><td> &lt; 0,987</td><td> 0,443 &lt;</td><td>in [131]</td><td> &lt; 0,445</td>

<td> 0,977 &lt;</td><td>in [94]</td><td> &lt; 0,979</td><td> 0,426 &lt;</td><td>in [132]</td><td> &lt; 0,428</td>

<td> 0,969 &lt;</td><td>in [95]</td><td> &lt; 0,971</td><td> 0,409 &lt;</td><td>in [133]</td><td> &lt; 0,411</td>

<td> 0,960 &lt;</td><td>in [96]</td><td> &lt; 0,962</td><td> 0,392 &lt;</td><td>in [134]</td><td> &lt; 0,394</td>

<td> 0,951 &lt;</td><td>in [97]</td><td> &lt; 0,953</td><td> 0,375 &lt;</td><td>in [135]</td><td> &lt; 0,377</td>

<td> 0,941 &lt;</td><td>in [98]</td><td> &lt; 0,943</td><td> 0,358 &lt;</td><td>in [136]</td><td> &lt; 0,360</td>

<td> 0,931 &lt;</td><td>in [99]</td><td> &lt; 0,933</td><td> 0,341 &lt;</td><td>in [137]</td><td> &lt; 0,343</td>

<td> 0,920 &lt;</td><td colspan="2">in [100] &lt;0.922</td><td> 0,325 &lt;</td><td>in [138]</td><td> &lt; 0,327</td>

<td> 0,909 &lt;</td><td colspan="2">in [101] &lt;0.911</td><td> 0,309 &lt;</td><td>in [139]</td><td> &lt; 0,311</td>

<td> 0,897 &lt;</td><td colspan="2">in [102] | &lt;0.899</td><td> 0,293 &lt;</td><td>in [140]</td><td> &lt; 0,295</td>

<td> 0,885 &lt;</td><td colspan="2">in [103] | &lt;0.887</td><td> 0,277 &lt;</td><td>in [141]</td><td> &lt; 0,279</td>

<td> 0,872 &lt;</td><td colspan="2">in [104] | &lt;0.879</td><td> 0,261 &lt;</td><td>in [142]</td><td> &lt; 0,263</td>

<td> 0,860 &lt;</td><td colspan="2">in [105] | &lt;0.862</td><td> 0,246 &lt;</td><td>in [143]</td><td> &lt; 0,248</td>

<td> 0,896 &lt;</td><td colspan="2">in [106] | &lt;0.848</td><td> 0,231 &lt;</td><td>in [144]</td><td> &lt; 0,233</td>

<td> 0,833 &lt;</td><td colspan="2">in [107] | &lt;0.835</td><td> 0,216 &lt;</td><td>in [145]</td><td> &lt; 0,218</td>

<td> 0,819 &lt;</td><td colspan="2">in [108] &lt;0.821</td><td> 0,201 &lt;</td><td>in [146]</td><td> &lt; 0,203</td>

<td> 0,804 &lt;</td><td colspan="2">in [109] | &lt;0.806</td><td> 0,187 &lt;</td><td>in [147]</td><td> &lt; 0,189</td>

<td> 0,790 &lt;</td><td colspan="2">in [110] | &lt;0.792</td><td> 0,173 &lt;</td><td>in [148]</td><td> &lt; 0,175</td>

<td> 0,775 &lt;</td><td colspan="2">in [111] | &lt;0.777</td><td> 0,159 &lt;</td><td>in [149]</td><td> &lt; 0,161</td>

<td> 0,145 &lt;</td><td colspan="2">in [150] &lt;0.147</td><td> 0,125 &lt;</td><td>in [188]</td><td> &lt; 0,127</td>

<td> 0,132 &lt;</td><td colspan="2">in [151] | &lt;0.134</td><td> 0,126 &lt;</td><td>in [189]</td><td> &lt; 0,128</td>

<td> 0,119 &lt;</td><td colspan="2">in [152] | &lt;0.121</td><td> 0,126 &lt;</td><td>in [190]</td><td> &lt; 0,128</td>

<td> 0,106 &lt;</td><td colspan="2">in [153] &lt;0.108</td><td> 0,126 &lt;</td><td>in [191]</td><td> &lt; 0,128</td>

<td> 0,094 &lt;</td><td colspan="2">in [154] &lt;0.096</td><td> 0,126 &lt;</td><td>in [192]</td><td> &lt; 0,128</td>

<td> 0,082 &lt;</td><td colspan="2">in [155] | &lt;0.084</td><td> 0,127 &lt;</td><td>in [193]</td><td> &lt; 0,129</td>

<td> 0,070 &lt;</td><td colspan="2">in [156] | &lt;0.072</td><td> 0,126 &lt;</td><td>in [199]</td><td> &lt; 0,128</td>

126

<td> 0,059 &lt;</td><td>in [157]</td><td> &lt; 0,061</td><td> 0,126 &lt;</td><td>in [195]</td><td> &lt; 0,128</td>

<td> 0,048 &lt;</td><td>in [158]</td><td> &lt; 0,050</td><td> 0,125 &lt;</td><td>in [196]</td><td> &lt; 0,127</td>

<td> 0,037 &lt;</td><td>in [159]</td><td> &lt; 0,039</td><td> 0,124 &lt;</td><td>in [197]</td><td> &lt; 0,126</td>

<td> 0,026 &lt;</td><td>in [160]</td><td> &lt; 0,028</td><td> 0,123 &lt;</td><td>in [198]</td><td> &lt; 0,125</td>

<td> 0,016 &lt;</td><td>in [161]</td><td> &lt; 0,018</td><td> 0,122 &lt;</td><td>in [199]</td><td> &lt; 0,129</td>

<td> 0,006 &lt;</td><td>in [162]</td><td> &lt; 0,008</td><td> 0,121 &lt;</td><td>in [200]</td><td> &lt; 0,123</td>

<td> 0,001 &lt;</td><td>in [163]</td><td> &lt; 0,003</td><td> 0,119 &lt;</td><td>in [201]</td><td> &lt; 0,121</td>

<td> 0,010 &lt;</td><td>in [164]</td><td> &lt; 0,012</td><td> 0,118 &lt;</td><td>in [202]</td><td> &lt; 0,120</td>

<td> 0,019 &lt;</td><td>in [165]</td><td> &lt; 0,021</td><td> 0,116 &lt;</td><td>in [203]</td><td> &lt; 0,118</td>

<td> 0,028 &lt;</td><td>in [166]</td><td> &lt; 0,030</td><td> 0,114 &lt;</td><td>in [204]</td><td> &lt; 0,116</td>

<td> 0,036 &lt;</td><td>in [167]</td><td> &lt; 0,038</td><td> 0,111 &lt;</td><td>in [205]</td><td> &lt; 0,113</td>

<td> 0,043 &lt;</td><td>in [168]</td><td> &lt; 0,045</td><td> 0,109 &lt;</td><td>in [206]</td><td> &lt; 0,111</td>

<td> 0,051 &lt;</td><td>in [169]</td><td> &lt; 0,053</td><td> 0,107 &lt;</td><td>in [207]</td><td> &lt; 0,109</td>

<td> 0,058 &lt;</td><td>in [170]</td><td> &lt; 0,060</td><td> 0,104 &lt;</td><td>in [208]</td><td> &lt; 0,106</td>

<td> 0,065 &lt;</td><td>in [171]</td><td> &lt; 0,067</td><td> 0,102 &lt;</td><td>in [209]</td><td> &lt; 0,104</td>

<td> 0,071 &lt;</td><td>in [172]</td><td> &lt; 0,073</td><td> 0,099 &lt;</td><td>in [210]</td><td> &lt; 0,101</td>

<td> 0,077 &lt;</td><td>in [173]</td><td> &lt; 0,079</td><td> 0,096 &lt;</td><td>in [211]</td><td> &lt; 0,098</td>

<td> 0,082 &lt;</td><td>in [174]</td><td> &lt; 0,084</td><td> 0,093 &lt;</td><td>in [212]</td><td> &lt; 0,095</td>

<td> 0,088 &lt;</td><td>in [175]</td><td> &lt; 0,090</td><td> 0,090 &lt;</td><td>in [213]</td><td> &lt; 0,092</td>

<td> 0,093 &lt;</td><td>in [176]</td><td> &lt; 0,095</td><td> 0,087 &lt;</td><td>in [214]</td><td> &lt; 0,089</td>

<td> 0,097 &lt;</td><td>in [177]</td><td> &lt; 0,099</td><td> 0,084 &lt;</td><td>in [215]</td><td> &lt; 0,086</td>

<td> 0,101 &lt;</td><td>in [178]</td><td> &lt; 0,103</td><td> 0,082 &lt;</td><td>in [216]</td><td> &lt; 0,084</td>

<td> 0,105 &lt;</td><td>in [179]</td><td> &lt; 0,107</td><td> 0,079 &lt;</td><td>in [217]</td><td> &lt; 0,081</td>

<td> 0,109 &lt;</td><td>in [180]</td><td> &lt; 0,111</td><td> 0,076 &lt;</td><td>in [218]</td><td> &lt; 0,078</td>

<td> 0,112 &lt;</td><td>in [181]</td><td> &lt; 0,114</td><td> 0,073 &lt;</td><td>in [219]</td><td> &lt; 0,075</td>

<td> 0,115 &lt;</td><td>in [182]</td><td> &lt; 0,117</td><td> 0,070 &lt;</td><td>in [220]</td><td> &lt; 0,072</td>

<td> 0,117 &lt;</td><td>in [183]</td><td> &lt; 0,119</td><td> 0,067 &lt;</td><td>in [221]</td><td> &lt; 0,069</td>

<td> 0,119 &lt;</td><td>in [189]</td><td> &lt; 0,121</td><td> 0,064 &lt;</td><td>in [222]</td><td> &lt; 0,066</td>

<td> 0,121 &lt;</td><td>in [185]</td><td> &lt; 0,123</td><td> 0,061 &lt;</td><td>in [223]</td><td> &lt; 0,063</td>

<td> 0,123 &lt;</td><td>in [186]</td><td> &lt; 0,125</td><td> 0,058 &lt;</td><td>in [224]</td><td> &lt; 0,060</td>

<td> 0,124 &lt;</td><td>in [187]</td><td> &lt; 0,126</td><td> 0,055 &lt;</td><td>in [225]</td><td> &lt; 0,057</td>

<td> 0,053 &lt;</td><td>in [226]</td><td> &lt; 0,055</td><td> 0,004 &lt;</td><td>in [264]</td><td> &lt; 0,006</td>

<td> 0,050 &lt;</td><td>in [227]</td><td> &lt; 0,052</td><td> 0,004 &lt;</td><td>in [265]</td><td> &lt; 0,006</td>

<td> 0,047 &lt;</td><td>in [228]</td><td> &lt; 0,049</td><td> 0,003 &lt;</td><td>in [266]</td><td> &lt; 0,005</td>

<td> 0,045 &lt;</td><td>in [229]</td><td> &lt; 0,047</td><td> 0,003 &lt;</td><td>in [267]</td><td> &lt; 0,005</td>

127

<td> 0,043 &lt;</td><td>in [230]</td><td> &lt; 0,045</td>

<td> 0,040 &lt;</td><td>in [231]</td><td> &lt; 0,042</td>

<td> 0,038 &lt;</td><td>in [232]</td><td> &lt; 0,040</td>

<td> 0,036 &lt;</td><td>in [233]</td><td> &lt; 0,038</td>

<td> 0,034 &lt;</td><td>in [234]</td><td> &lt; 0,036</td>

<td> 0,032 &lt;</td><td>in [235]</td><td> &lt; 0,034</td>

<td> 0,030 &lt;</td><td>in [236]</td><td> &lt; 0,032</td>

<td> 0,028 &lt;</td><td>in [237]</td><td> &lt; 0,030</td>

<td> 0,027 &lt;</td><td>in [238]</td><td> &lt; 0,029</td>

<td> 0,025 &lt;</td><td>in [239]</td><td> &lt; 0,027</td>

<td> 0,023 &lt;</td><td>in [240]</td><td> &lt; 0,025</td>

<td> 0,022 &lt;</td><td>in [241]</td><td> &lt; 0,024</td>

<td> 0,021 &lt;</td><td>in [242]</td><td> &lt; 0,023</td>

<td> 0,019 &lt;</td><td>in [243]</td><td> &lt; 0,021</td>

<td> 0,018 &lt;</td><td>in [244]</td><td> &lt; 0,020</td>

<td> 0,017 &lt;</td><td>in [245]</td><td> &lt; 0,019</td>

<td> 0,016 &lt;</td><td>in [296]</td><td> &lt; 0,018</td>

<td> 0,015 &lt;</td><td>in [247]</td><td> &lt; 0,017</td>

<td> 0,014 &lt;</td><td>in [298]</td><td> &lt; 0,016</td>

<td> 0,013 &lt;</td><td>in [249]</td><td> &lt; 0,015</td>

<td> 0,012 &lt;</td><td>in [250]</td><td> &lt; 0,014</td>

<td> 0,011 &lt;</td><td>in [251]</td><td> &lt; 0,013</td>

<td> 0,010 &lt;</td><td>in [252]</td><td> &lt; 0,012</td>

<td> 0,009 &lt;</td><td>in [253]</td><td> &lt; 0,011</td>

<td> 0,009 &lt;</td><td>in [254]</td><td> &lt; 0,011</td>

<td> 0,008 &lt;</td><td>in [255]</td><td> &lt; 0,010</td>

<td> 0,007 &lt;</td><td>in [256]</td><td> &lt; 0,009</td>

<td> 0,007 &lt;</td><td>in [257]</td><td> &lt; 0,009</td>

<td> 0,006 &lt;</td><td>in [258]</td><td> &lt; 0,008</td>

<td> 0,006 &lt;</td><td>in [259]</td><td> &lt; 0,008</td>

<td> 0,006 &lt;</td><td>in [260]</td><td> &lt; 0,008</td>

<td> 0,005 &lt;</td><td>in [261]</td><td> &lt; 0,007</td>

<td> 0,005 &lt;</td><td>in [262]</td><td> &lt; 0,007</td>

<td> 0,004 &lt;</td><td>in [263]</td><td> &lt; 0,006</td>

<td> 0,000 &lt;</td><td>in [302]</td><td> &lt; 0,002</td>

0.003 &lt;| in [268] &lt;0.005 0.003 &lt; in [269] &lt;0.005 0.002 &lt; in [270] | &lt;0.004 0.002 &lt;| in [271] &lt;0.009 0.002 &lt; in [272] &lt;0.004 0.001 &lt;| in [273] &lt;0.003 0.001 &lt;| in [274] | &lt;0.003 0.001 &lt;| in [275] &lt;0.003 0.001 &lt;| in [276] &lt;0.003 0.000 &lt;| in [277] &lt;0.002 0.000 &lt;| in [278] | &lt;0.002 0.000 &lt;| in [279] &lt;0.002 0.000 &lt;| in [280] &lt;0.002 0.000 &lt;| in [281] &lt;0.002 0.000 &lt;| in [282] | &lt;0.002 -0.001 &lt;| in [283] | &lt;0.001 -0.001 &lt;| in [284] &lt;0.001 -0.001 &lt;| in [285] &lt;0.001 -0.001 &lt;| in [286] &lt;0.001 0.000 &lt;| in [287] &lt;0.002 0.000 &lt;| in [288] | &lt;0.002 0.000 &lt;| in [289] &lt;0.002 0.000 &lt;| in [290] &lt;0.002 0.000 &lt;| in [291] &lt;0.002 0.001 &lt;| in [292] &lt;0.003 0.001 &lt;| in [293] &lt;0.003 0.001 &lt;| in [294] &lt;0.003 0.001 &lt;| in [295] &lt;0.003 0.000 &lt;| in [296] | &lt;0.002 0.000 &lt;| in [297] &lt;0.002 0.000 &lt;| in [298] &lt;0.002 -0.001 &lt;| in [299] &lt;0.001 -0.001 &lt;| in [300] &lt;0.001 0.000 &lt;| in [301] | &lt;0.002 0.000 &lt;| in [340] &lt;0.002

128

0.001 &lt;| in [303] &lt;0.003 0.001 &lt;| in [304] &lt;0.003 0.002 &lt; in [305] | &lt;0.004 0.002 &lt;| in [306] &lt;0.004 0.002 &lt;| in [307] &lt;0.004 0.003 &lt; in [308] | &lt;0.005 0.003 &lt; in [309] &lt;0.005 0.003 &lt; in [310] &lt;0.005 0.004 &lt; in [311] &lt;0.006 0.004 &lt; in [312] | &lt;0.006 0.004 &lt; in [313] | &lt;0.006 0.004 &lt; in [314] | &lt;0.006 0.004 &lt; in [315] &lt;0.006 0.004 &lt; in [316] &lt;0.006 0.003 &lt;| in [317] | &lt;0.005 0.003 &lt; in [318] | &lt;0.005 0.003 &lt; in [319] &lt;0.005 0.003 &lt; in [320] | &lt; 0.005 0.002 &lt;| in [321] &lt;0.009 0.002 &lt; in [322] | &lt;0.004 0.002 &lt;| in [323] | &lt;0.004 0.001 &lt;| in [324] | &lt;0.003 0.001 &lt;| in [325] &lt;0.003 0.001 &lt;| in [326] | &lt;0.003 0.000 &lt;| in [327] | &lt;0.002 0.000 &lt;| in [328] | &lt;0.002 -0.001 &lt;| in [329] &lt;0.001 -0.001 &lt;| in [330] | &lt;0.001 -0.001 &lt;| in [331] &lt;0.001 -0.001 &lt;| in [332] &lt;0.001 -0.001 &lt;| in [333] | &lt;0.001 0.000 &lt;| in [334] | &lt;0.002 0.000 &lt;| in [335] | &lt;0.002 0.000 &lt;| in [336] &lt;0.002 0.000 &lt;| in [337] &lt;0.002

0.000 &lt;| in [341] &lt;0.002 0.000 &lt;| in [342] | &lt;0.002 0.000 &lt;| in [343] | &lt;0.002 -0.001 &lt;| in [344] | &lt;0.001 -0.001 &lt;| in [345] | &lt;0.001 0.000 &lt;| in [396] &lt;0.002 0.000 &lt;| in [347] &lt;0.002 0.001 &lt;| in [348] | &lt;0.003 0.001 &lt;| in [349] &lt;0.003 0.001 &lt;| in [350] | &lt;0.003 0.002 &lt; in [351] | &lt;0.004, 0.002 &lt;| in [352] &lt;0.004 0.002 &lt;| in [353] | &lt;0.004 0.002 &lt;| in [354] | &lt;0.004 0.002 &lt;| in [355] &lt;0.004 0.001 &lt;| in [356] &lt;0.003 0.001 &lt;| in [357] &lt;0.003 0.001 &lt;| in [358] &lt;0.003 0.001 &lt;| in [359] &lt;0.003 0.001 &lt;| in [360] | &lt;0.003 0.000 &lt;| in [361] &lt;0.002 0.000 &lt;| in [362] &lt;0.002 0.000 &lt;| in [363] &lt;0.002 -0.001 &lt;| in [364] | &lt;0.001 -0.001 &lt;| in [365] | &lt;0.001 -0.001 &lt;| in [366] &lt;0.001 -0.001 &lt;| in [367] &lt;0.001 0.000 &lt;| in [368] | &lt;0.002 0.000 &lt;| in [369] &lt;0.002 0.000 &lt;| in [370] | &lt;0.002 0.000 &lt;| in [371] &lt;0.002 0.000 &lt;| in [372] &lt;0.002 0.000 &lt;| in [373] &lt;0.002 0.000 &lt;| in [374] &lt;0.002 0.000 &lt;| in [375] &lt;0.002

129

<td> 0,000 &lt; |</td><td>in [338] &lt;0.002</td><td>0.000 &lt;| in [376]</td><td> &lt; 0,002</td>

<td> 0,000 &lt; |</td><td>in [339] | &lt;0.002</td><td colspan="2">0.000 &lt;| in [377] &lt;0.002</td>

<td> 0,000 &lt; |</td><td>in [378] | &lt;0.002</td><td>-0.001 &lt;| and [416]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [379] &lt;0.002</td><td>-0.001 &lt;| and [417]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [380] | &lt;0.002</td><td>-0.001 &lt;| and [418]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [381] &lt;0.002</td><td>-0.001 &lt;| and [419]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [382] &lt;0.002</td><td>-0.001 &lt;| and [420]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [383] &lt;0.002</td><td>-0.001 &lt;| and [421]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [384] &lt;0.002</td><td>-0.001 &lt;| and [422]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [385] | &lt;0.002</td><td>-0.001 &lt;| and [423]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [386] &lt;0.002</td><td>-0.001 &lt;| and [424]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [387] &lt;0.002</td><td>-0.001 &lt;| and [425]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [388] &lt;0.002</td><td>-0.001 &lt;| and [426]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [389] &lt;0.002</td><td>-0.001 &lt;| and [927]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [390] &lt;0.002</td><td>-0.001 &lt;| and [428]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [391] &lt;0.002</td><td>-0.001 &lt;| and [429]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [392] &lt;0.002</td><td>-0.001 &lt;| and [430]</td><td> &lt; 0,001</td>

<td> 0,000 &lt; |</td><td>in [393] | &lt;0.002</td><td>-0.001 &lt;| and [431]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [394] &lt;0.001</td><td>-0.001 &lt;| and [432]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [395] &lt;0.001</td><td>-0.001 &lt;| and [433]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [396] &lt;0.001</td><td>-0.001 &lt;| and [434]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [397] &lt;0.001</td><td>-0.001 &lt;| and [435]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [398] &lt;0.001</td><td>-0.001 &lt;| and [436]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [399] &lt;0.001</td><td>-0.001 &lt;| and [437]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [400] &lt;0.001</td><td>-0.001 &lt;| and [938]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [401] | &lt;0.001</td><td>-0.001 &lt;| and [439]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [402] &lt;0.001</td><td>-0.001 &lt;| and [440]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [403] | &lt;0.001</td><td>-0.001 &lt;| and [441]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [404] &lt;0.001</td><td>-0.001 &lt;| and [442]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [405] | &lt;0.001</td><td>-0.001 &lt;| and [943]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [406] &lt;0.001</td><td>-0.001 &lt;| and [444]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [407] &lt;0.001</td><td>-0.001 &lt;| and [445]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [408] | &lt;0.001</td><td>-0.001 &lt;| and [446]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [409] &lt;0.001</td><td>-0.001 &lt;| and [447]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>| in [410] &lt;0.001</td><td>-0.001 &lt;| and [448]</td><td> &lt; 0,001</td>

130

<td> -0,001 &lt;</td><td>| and [411]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [449]</td>

<td> -0,001 &lt;</td><td>| and [912]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [450]</td>

<td> -0,001 &lt;</td><td>| and [413]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [451]</td>

<td> -0,001 &lt;</td><td>| and [414]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [452]</td>

<td> -0,001 &lt;</td><td>| and [415]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [453]</td>

<td> -0,001 &lt;</td><td>| and [454]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [492]</td>

<td> -0,001 &lt;</td><td>| and [455]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [493]</td>

<td> -0,001 &lt;</td><td>| and [456]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [994]</td>

<td> -0,001 &lt;</td><td>| and [457]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [995]</td>

<td> -0,001 &lt;</td><td>| and [958]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [996]</td>

<td> -0,001 &lt;</td><td>| and [959]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [497]</td>

<td> -0,001 &lt;</td><td>| and [460]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [498]</td>

<td> -0,001 &lt;</td><td>| and [461]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [999]</td>

<td> -0,001 &lt;</td><td>| and [462]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [500]</td>

<td> -0,001 &lt;</td><td>| and [463]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [501]</td>

<td> -0,001 &lt;</td><td>| and [464]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [502]</td>

<td> -0,001 &lt;</td><td>| and [465]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [503]</td>

<td> -0,001 &lt;</td><td>| and [466]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [504]</td>

<td> -0,001 &lt;</td><td>| and [467]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [505]</td>

<td> -0,001 &lt;</td><td>| and [468]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [506]</td>

<td> -0,001 &lt;</td><td>| and [969]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [507]</td>

<td> -0,001 &lt;</td><td>| and [470]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [508]</td>

<td> -0,001 &lt;</td><td>| and [471]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [509]</td>

<td> -0,001 &lt;</td><td>| and [472]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [510]</td>

<td> -0,001 &lt;</td><td>| and [473]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [511]</td>

<td> -0,001 &lt;</td><td>| and [474]</td><td> | &lt;0,001</td><td> -0,001 &lt;</td><td>and [512]</td>

<td> -0,001 &lt;</td><td>| and [475]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [513]</td>

<td> -0,001 &lt;</td><td>| and [476]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [514]</td>

<td> -0,001 &lt;</td><td>| and [477]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [515]</td>

<td> -0,001 &lt;</td><td>| and [478]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [516]</td>

<td> 0,000 &lt; |</td><td>in [479]</td><td> &lt; 0,002</td><td> -0,001 &lt;</td><td>and [517]</td>

<td> -0,001 &lt;</td><td>| and [480]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [518]</td>

<td> -0,001 &lt;</td><td>| and [481]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [519]</td>

<td> -0,001 &lt;</td><td>| and [482]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [520]</td>

<td> -0,001 &lt;</td><td>| and [483]</td><td> | &lt; 0,001</td><td> -0,001 &lt;</td><td>| and [521]</td>

&lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001 &lt; 0,001

131

<td> -0,001 &lt;</td><td>and [484]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [522]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [485]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [523]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [486]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [524]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [487]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [525]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [488]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [526]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [489]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [527]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [490]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [528]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [991]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [529]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [530]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [568]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [531]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [569]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [532]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [570]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [533]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [571]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [534]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [572]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [535]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [573]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [536]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [574]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [537]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [575]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [538]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [576]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [539]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [577]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [540]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [578]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [541]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [579]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [542]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [580]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [543]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [581]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [544]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [582]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [545]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [583]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [546]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [584]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [547]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [585]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [548]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [586]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [549]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [587]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [550]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [588]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [551]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [589]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [552]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [590]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [553]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [591]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [554]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [592]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [555]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [593]</td><td> &lt; 0,001</td>

<td> -0,001 &lt;</td><td>and [556]</td><td> &lt; 0,001</td><td> -0,001 &lt;</td><td>and [594]</td><td> &lt; 0,001</td>

132

0.001 &lt;| in [557] &lt;0.001 0.001 &lt; in [558] | &lt;0.001 0.001 &lt; in [559] | &lt;0.001 0.001 &lt; in [560] | &lt;0.001 0.001 &lt; in [561] | &lt;0.001 0.001 &lt; in [562] | &lt;0.001 0.001 &lt; in [563] | &lt;0.001 0.001 &lt; in [564] | &lt;0.001 0.001 &lt; in [565] | &lt;0.001 0.001 &lt; in [566] &lt;0.001 0.001 &lt; in [567] | &lt;0.001 0.001 &lt; in [606] | &lt;0.001 0.001 &lt; in [607] | &lt;0.001 0.001 &lt; in [608] | &lt;0.001 0.001 &lt; in [609] &lt;0.001 0.001 &lt; in [610] | &lt;0.001 0.001 &lt; in [611] &lt;0.001 0.001 &lt; in [612] | &lt;0.001 0.001 &lt; in [613] &lt;0.001 0.001 &lt; in [619] &lt;0.001 0.001 &lt; in [615] &lt;0.001 0.001 &lt; in [616] &lt;0.001 0.001 &lt; in [617] | &lt;0.001 0.001 &lt; in [618] &lt;0.001 0.001 &lt; in [619] &lt;0.001 0.001 &lt; in [620] &lt;0.001 0.001 &lt; in [621] &lt;0.001 0.001 &lt; in [622] | &lt;0.001

-0.001 &lt;| in [595] &lt;0.001 -0.001 &lt;| in [596] &lt;0.001 -0.001 &lt;| in [597] &lt;0.001 -0.001 &lt;| in [598] &lt;0.001 -0.001 &lt;| in [599] &lt;0.001 -0.001 &lt;| in [600] | &lt;0.001 -0.001 &lt;| in [601] &lt;0.001 0.001 &lt; in [602] | &lt;0.001 -0.001 &lt;| in [603] | &lt;0.001 -0.001 &lt;| in [604] | &lt;0.001 -0.001 &lt;| in [605] | &lt;0.001 -0.001 &lt;| in [623] | &lt;0.001 -0.001 &lt;| in [624] | &lt;0.001 -0.001 &lt;| in [625] | &lt;0.001 -0.001 &lt;| in [626] &lt;0.001 -0.001 &lt;| in [627] &lt;0.001 -0.001 &lt;| in [628] &lt;0.001 -0.001 &lt;| in [629] &lt; 0.001 -0.001 &lt;| in [630] | &lt;0.001 -0.001 &lt;| in [631] | &lt;0.001 -0.001 &lt;| in [632] | &lt;0.001 -0.001 &lt;| in [633] &lt;0.001 -0.001 &lt;| in [634] &lt;0.001 -0.001 &lt;| in [635] &lt;0.001 -0.001 &lt;| in [636] &lt;0.001 -0.001 &lt;| in [637] &lt;0.001 -0.001 &lt;| in [638] &lt;0.001 -0.001 &lt;| in [639] &lt;0.001

FRAUNHOFER-GESELLSCHAFT ZUR FORDERUNG DER ANGEWANDTEN FORSCHUNG EV, GERMANY

PROXY:

133

EP 1 994 530 B1

Z - 6137/09