Filterbank for spectrally modifying a digital signal and corresponding method

0001Method and filter bank for the spectral modification of a digital signal

0002The invention relates to a method for the spectral modification of a digital signal, in particular an audio signal, as well as a filter bank for the corresponding spectral modification of the digital signal.

0003Methods for the spectral modification of a digital signal are used in modern digital signal processing for a variety of purposes. Typical applications include digital cellular systems and speech recognition systems. It is usually about improving disturbed speech signals with the help of digital speech signal processing. For example, previously measured frequency responses of certain input or output modules, such as the handset or loudspeaker of a mobile device, can be compensated for by appropriate pre- or post-filtering of the signal in order to obtain an optimum input or output signal. A typical embodiment of this is a so-called "Graphic Equalizer". Furthermore, for example, by a constant adaptation of the filter characteristics to the signal to be modified originally recorded with the speech signal background noise, eg. B. when using a speakerphone in a car phone, or by the transmission in a mobile network caused interference of the signal by appropriate spectral modification, ie filtering, eliminated or at least greatly reduced.

0004In order to spectrally modify a digital signal, it is in principle possible to pass this signal through a certain number of bandpasses, through each bandpass exactly a certain frequency range is passed and the remaining frequency ranges are filtered out. This is shown as an example in FIG. The starting point in this figure is an input signal x (k) to be modified, which z. B. by an equidistant sampling of a continuous time signal, such as a microphone voltage, at different times t = k · T may have arisen, where T is the so-called sampling period of the signal. The signal x (k) is thus a sequence of numbers numbered "k". By the filter shown in Figure 1, the signal x (k) with N + 1 bandpass filters, each having the impulse response h_i(k), in N + 1 subband signals y_i(k), i = 0,1, ..., N decomposed. This can be represented mathematically by the following equation:<maths id="math0001" num=""><img file="EP1538749A2_D0001.tif" /></maths>

0005The desired spectral modification of the input signal x (k) is then achieved by dividing each subband signal by an individual weighting coefficient or "gain multiplier" g_i, i = 0,1, ..., N, is multiplied. The output signal y (k) is then obtained by superposition of the weighted subband signals according to<maths id="math0002" num=""><img file="EP1538749A2_D0002.tif" /></maths>

0006In addition to a frequency smoothing - for example, to compensate for the frequency response of certain other components within a signal transmission chain or to adapt a signal to the human ear - an adaptive noise reduction with such filters is basically possible. In the first case, the weighting factors g_i be constant, but with adaptive noise reduction, these factors must vary over time. The weighting factors g_i, for which usually 0 ≤ g_i ≤ 1, ensure in each case for a different attenuation of the individual frequency bands. For adaptive noise reduction, the individual weighting factors g_i in each case separately on the basis of the signal to be modified, for example in the spectral range, and from the current signal / noise ratio of each individual subband signal y_i(k) depend.

0007An essential problem of the "reference filter bank" system shown in FIG. 1 is that N + 1 separate band filters are required for this purpose. This is on the one hand extremely computationally expensive and on the other hand very expensive. Therefore, in real applications for spectral modification usually so-called analysis-synthesis systems are used. Such a system is shown schematically in FIG. The input signal x (k) is first supplied to a spectral analysis, in which the signal is decomposed into suitably selected basic components. This is done with the aid of a so-called time / spectral transformation, for example a Fourier transformation or a discrete Fourier transformation (DFT), a z transformation, a discrete cosine transformation (DCT) or the like. After this transformation of the input signal x (k) from the time domain into the spectral domain, a so-called spectral subtraction takes place, wherein, mathematically speaking, the individual spectral components X_μ(k), μ = 0,1, ... M-1 each with certain factors, the so-called frequency response H_μ(k) are weighted in the relevant frequency range. The thus produced modified spectral components Ŝ_μ(k) are then fed to a so-called spectral synthesis, in which the signal components Ŝ_μ(k) are again superimposed on each other to produce the output signal y (k). This spectral synthesis is carried out with a so-called spectral / time transformation, ie an inverse time / spectral transformation, for example with an Inverse Discrete Fourier Transform (IDTF), an Inverse Discrete Cosine Transform (IDCT) or an Inverse z-Transformation, etc. the signal is transformed back into the time domain. A problem with these conventional signal processing methods is that an analysis-synthesis system is to be designed primarily for the re-synthesis of the signal. In particular, it should be ensured that refolding (so-called "aliasing") by clock reduction after analysis and by non-ideal interpolations in the course of the synthesis are avoided. Otherwise, unwanted effects such as distortion and reverberation in the interfering output signal may occur. These requirements lead to an increased computational effort and to an increased delay of the entire filter system.

0008It is therefore an object of the present invention to provide a simple and inexpensive alternative to the known prior art in which, in particular, the refolding problems and the signal delay through the system are reduced.

0009This object is achieved by a method according to claim 1 and by a filter bank according to claim 10.

0010According to the invention, in this method, the digital signal is filtered with an equivalent time domain filter having an effective sum impulse response by - in the time domain - the digital signal being passed through a delay chain with a number of delay stages and at the delay chain, ie Before and / or after the delay chain and / or between the delay stages tapped signal components are each passed through a filter unit with a weighted low-pass prototype impulse response and the signal components are then added up again. That is to say that signal blocks of a specific length are formed by the delay chain from the input signal and are then processed by the filter unit. An "equivalent time domain filter" is a single filter whose frequency response coincides with the sum frequency response of a filter bank with weighting of the subband signals. Accordingly, the term "effective aggregate impulse response" is understood to mean an impulse response of a single filter that matches the sum of the weighted impulse responses of the bandpass filters of a filterbank, and "lowpass prototype impulse response" is understood to be an impulse response of a lowpass filter from which the impulse responses a filter bank are generated by modulation.

0011For this purpose, a corresponding filter bank must have an equivalent time domain filter for filtering the digital signal with an effective sum impulse response, which has a delay chain with a number of delay stages in order to stepwise delay the digital signal to be modified and a filter unit connected downstream of the delay chain, which filters signal portions tapped on the delay chain, each with a weighted low-pass prototype impulse response, and a summer means for producing an output signal from the filtered signal components.

0012Consequently, a decisive advantage of the method and construction according to the invention is that, in order to filter a digital input signal in any desired manner, it is ultimately sufficient to construct only one filter with a specific low-pass prototype impulse response. Only a corresponding weighting of this low-pass prototype impulse response is required. The weighting is preferably carried out with a so-called window function, ie with a certain weight sequence, which may be constant to build a constant filter, or may be variable to build an adaptive filter. The filtering takes place directly in the time domain. The system is thus characterized by a low signal delay.

0013The dependent claims each contain particularly advantageous embodiments and developments of the invention, wherein in particular the filter bank according to the invention can also be developed according to the method claims and vice versa.

0014In order to adapt the weighting factors to the achievement of a specific filtering target to the signal or a background signal or the like, the window function is preferably obtained according to a predetermined rule from the signal to be modified or the external signal. In contrast to filtering with constant weighting factors, adaptive filtering is thus easily possible. For this purpose, the filter bank according to the invention must additionally be equipped with a corresponding window function calculation device, which then determines the window function according to the predetermined rule from the signal to be modified or the external signal.

0015An easy way to implement this method or structure is to first decouple the signal to be modified similar to the classical analysis-synthesis method on the input side and transform it into the spectral range and to calculate the weighting coefficients in the spectral range. Under determination of the window function, the weighting coefficients of the spectral range can then be transformed back into the time domain and then used in the time domain to weight the low-pass prototype impulse response. Although the calculation of the coefficients requires a similar effort as in the conventional analysis-synthesis systems, nevertheless the entire filter system has a considerably lower delay because the filtering or As a rule, convolution of the signal does not have to wait for the coefficients to be calculated, since the coefficients are normally relatively slowly variable anyway. Moreover, it can not come to the spectral refolding, since here only the window function, ie the weighting coefficients, are transformed back and not the signal itself.

0016A corresponding window function calculation unit should firstly have a time / spectral transformation device in order to transform the signal to be modified and / or the external signal into the spectral range. Moreover, a weighting coefficient calculating means is required to obtain the weighting coefficients on the basis of the transformed signal to be modified and / or external signal. Finally, a spectral / time transformation device is necessary in order to transform the weighting coefficients from the spectral region to the time domain while determining the window function.

0017In principle, arbitrary time / spectral transformations or inverse time / spectral transformations can be used in this case, such as. As the z-transformation, the so-called Hadamar transformation or the Walsch transformation or the inverse thereof. However, it has been found that the discrete Fourier transformation and, accordingly, the inverse discrete Fourier transformation and the discrete cosine transformation or Inverse discrete cosine transformations are particularly suitable since they have the best transformation properties. However, the transformation properties ultimately also determine the filter properties of the overall system, so that the best filter properties can be achieved with these transformation methods.

0018If a discrete Fourier transformation is used, it makes sense to use the so-called "fast Fourier transformation" (FFT) for reasons of speed. To get the best result, the back and forth transformation to calculate the weighting functions should each be done with the same transformation type.

0019In the determination of the window function, a signal block of the input signal which is currently processed in the filter and is formed by means of a delay chain is preferably taken into account. Thus, the weighting factors can be advantageously calculated using the weighted state variables of the time domain filter. The state variables are the sampling values ​​of the input signal currently present in the delay chain of the time domain filter. For this purpose, the window function calculating device particularly preferably has a delay chain for the input signal corresponding to the delay chain of the equivalent time domain filter. Alternatively or additionally, a number of preceding signal blocks processed in the filter can also be taken into account, ie For example, additionally or exclusively, the weighted state variables of the time domain filter of one or more preceding signal blocks of the input signal are calculated.

0020For one thing, the delay stages within the delay chain may be preferably configured to delay the signal by exactly one sample period of the signal to be modified. This shifts the signal by exactly one sample each time. As a result, a uniform frequency resolution of the filter is achieved. On the other hand, it is also possible to construct the filter bank so that there is an uneven spectral resolution. This offers the possibility of adapting the signal within the filter system with respect to the frequency resolution, for example, to the human ear.

0021Such a frequency distortion of the filter bank can be achieved in a particularly simple manner if the delay stages are selected such that at least some of the delay stages have a so-called all-pass transfer function. Although such so-called "first-order allpass filters" allow all frequencies to pass through uniformly, the phase is changed in a frequency-dependent manner. With a simple replacement of the constant delay stages by delay stages with all-pass transfer function, it is possible, for example, to achieve as precisely as possible the non-uniform frequency resolution of the ear.

0022The method according to the invention or the filter bank according to the invention can in principle be used in any digital signal processing equipment for processing any digital signals. However, one main area of ​​application is in the field of voice and other audio signals. The use of the method according to the invention and the filter bank according to the invention in the field of receivers or transmitters in mobile radio networks, ie both within mobile devices and within network components of the mobile network, such as mobile base stations or mobile switching equipment.

0023The invention will be explained in more detail below with reference to the accompanying figures with reference to embodiments. Show it:<ul id="ul0001" list-style="none"><li>FIG. 1 shows a schematic representation of a classical reference filter bank with N + 1 different bandpass filters,</li><li>FIG. 2 shows a schematic representation of a conventional analysis-synthesis system for noise reduction,</li><li>FIG. 3 shows a schematic representation of a filter bank according to the invention with an equivalent time domain filter and a window function calculation device,</li><li>FIG. 4 shows a schematic illustration of the transfer functions of a cosine-modulated reference filter bank according to FIG. 1,</li><li>FIG. 5 a schematic representation of a first exemplary embodiment of an equivalent time domain filter of a filter bank according to the invention according to FIG. 3,</li><li>FIG. 6 a schematic representation of a second embodiment of an equivalent time domain filter of a filter bank according to the invention according to FIG. 3,</li><li>FIG. 7 shows a representation of a non-uniform frequency distortion with the aid of an all-pass transformation,</li><li>8 shows a representation of the effect of the frequency distortion by means of the all-pass transformation according to FIG. 7 on the frequency responses of different bandpass filters, FIG.</li><li>FIG. 9 shows a representation of the Bark scale on the frequency scale for the representation of the aurally correct frequency resolution according to the sound resolution,</li><li>FIG. 10 shows a first exemplary embodiment of a window function calculating device for a filter bank according to the invention according to FIG. 3,</li><li>11 is a schematic representation of the first part of a second exemplary embodiment of a window function calculating device for a filter bank according to the invention according to FIG. 3.</li></ul>

0024Based on a comparison between the schematic representations of the different filter bank concepts in Figures 1 to 3 is very well the difference of the filter bank 1 and the inventive method over the commonly used analysis-synthesis systems (Figure 2) and one of N + 1 single Bandpass filters constructed reference filter bank (Figure 1) clearly. The modes of operation of this reference filter bank according to FIG. 1 and the analysis-synthesis method, in which first the entire signal is subjected to spectral analysis, then a spectral subtraction is performed in the spectral range and then the signal components are synthesized again, have already been described in more detail above.

0025In contrast, in the method according to the invention, the input signal x (k) in the time domain, ie without previous spectral analysis, fed to an equivalent time domain filter 2 and there folded or filtered with a sum impulse response. This sum impulse response arises from the convolution of a low-pass prototype impulse response h (k) with a weight sequence, ie window function w (k). This results directly in the desired output signal y (k).

0026The exemplary embodiment illustrated in FIG. 3 is a filter 2 for the adaptive modification of the input signal x (k) as a function of the respective input signal x (k) to be modified, for example for noise suppression. Therefore, here the window function w (k) is obtained from the input signal x (k) itself. This is done in a window function calculation device 3, which for this purpose has a time / spectral transformation device 10 in order to transform the input signal x (k) into the spectral range. In a weighting coefficient calculation device 11, weighting coefficients g are then extracted from the transformed input signal in the spectral range₀,...,G_N calculated. These weighting coefficients g₀,...,G_N Finally, in a spectral / time transformation device 12, for example here by means of a discrete Fourier transform (DFT), transformed back into the time domain. The result is the desired window function w (k). This can then be convolved in the equivalent time domain filter 2 with the low pass prototype impulse response h (k) and the input signal.

0027Alternatively, an adaptive calculation of the window function w (k) could also be determined using another external signal, for example, a separately measured background noise signal or the like.

0028If a fixed filter characteristic is desired, the window function w (k) can also be implemented permanently in the filter, for example in order to achieve a signal adaptation to the human ear or to compensate for unfavorable frequency responses of other components present in the signal line.

0029In the following, it will be explained with reference to a specific example that the filtering achieved with the method or system shown schematically in FIG. 3 corresponds exactly to the filtering which is achieved even with the reference filter bank according to FIG. 1 constructed very costly with N + 1 different bandpasses in the time domain , For the starting point of the considerations, it is assumed that the individual bandpass filters of the reference filter bank according to FIG. 1 each consist of an FIR prototype low-pass filter of length n with an impulse response h (k) with k = 0.1..., N-1 by means of a cosine Are derived modulation. (FIR = finite impulse response, which means that it is a non-recursive filter). It then applies<maths id="math0003" num=""><img file="EP1538749A2_D0003.tif" /></maths> for k = 0,1, ... n-1. Where k₀ a constant delay value or phase parameter.

0030By means of a usual Fourier transformation, the corresponding frequency responses (transfer functions) of these impulse responses are obtained as follows:<maths id="math0004" num=""><img file="EP1538749A2_D0004.tif" /></maths>

0031FIG. 4 shows a schematic representation of these frequency responses. The amount of the frequency response | H is plotted in each case_i|, i = 0,1, ..., N, above the frequency normalized to π Ω.

0032It is further assumed that the weighting factors g_i at least for a short limited period of time. This assumption is admissible, since in practice in the case of adaptive filtering, too, the coefficients which indeed correspond to the disturbances to be filtered out are, as a rule, only very slowly variable relative to the actual signal.

0033In this case, the reference filter bank system shown in Figure 1 can be considered as a linear system. Therefore, this system can also be characterized by a total impulse response h_s(k) which is the sum of the individually scaled impulse responses h_i(k), ie:<maths id="math0005" num=""><img file="EP1538749A2_D0005.tif" /></maths>

0034As the last two lines in equation (4) show, the complete reference filter bank according to the present invention can be replaced by a single equivalent time domain filter. The effective total impulse response h_s(k) is the product of the prototype low-pass impulse response h (k) with a weight function w (k).

0035One possibility of technically implementing a corresponding equivalent time domain filter 2 in a very simple manner is shown in FIG. Here, the input signal x (k) in the time domain in a delay chain 8 with a number of n-1 delay stages 4 is fed. In this delay chain 8 takes place in the embodiment shown in Figure 5 in each of the delay stages 4, a delay to the delay operator z^-1, This is the delay operator of the z-transformation, which should symbolize a signal shift by the sampling interval T. That is, the incoming signal x (k) is shifted one sample at a time. Due to the delay of the signal x (k) in the delay chain 8 consequently a signal block (also called "frame" or "sample") is temporarily stored. Such delay chains 8 are therefore often called "memory chains". The length of the signal block is higher by 1 than the number of n-1 delay stages 4. In the illustrated example, signal blocks of the input signal x (k) of length n are respectively formed. A signal block is then further filtered in a (block) filter unit 6 first with the low-pass prototype impulse response h (k), wherein the memory chain with the delay stages 4, each signal value x (k), k = 0, ... , n-1 is multiplied by the corresponding value of the low-pass prototype impulse response h (k). This results in a total of n different signal values ​​x₀, x₁, ... x_k, ..., x_n-1, which are multiplied in a further step in the filter 6 with the individual function values ​​w (k), = 0, ..., κ, ..., n-1, ie weighted. Subsequently, a superimposition of the signal components in a summing device 7, whereby the desired output signal y (k) results.

0036Based on the example used at the outset, it can further be shown that a window function w (k) can be determined without problems by means of a discrete Fourier transformation, in particular a fast Fourier transformation, so that with a suitable choice of the low-pass prototype impulse response h (k ) also a perfect reconstruction of the signal x (k) in the time domain filter 2 can be achieved. Ie. that with a choice of weighting coefficients g_i = 1 for i = 0,1, ..., n-1 outputs the entire system as an output signal - apart from a constant delay - again outputs the input signal x (k).

0037Due to the behavior of the cosine function, the window function w (k) is always symmetric (see equation (4)). Ie. the window function w (k) is not limited in time according to the following definition:<maths id="math0006" num="(5)"><math display="block"><mrow><mtext>w (k + λ · 2N) = w (k); λ = constant ∈ {1,2,3, ...}</mtext></mrow></math><img file="EP1538749A2_D0006.tif" /></maths>

0038Only for the following considerations, the number N + 1 of the weighting coefficients g_i in the reference filter bank of Figure 1 artificially to a number M = 2N according to the rule<maths id="math0007" num=""><img file="EP1538749A2_D0007.tif" /></maths> extended. The window function w (k) can then be represented mathematically as follows:<maths id="math0008" num=""><img file="EP1538749A2_D0008.tif" /></maths>

0039This proves that the window function w (k) can be calculated by means of a discrete Fourier transformation or a fast Fourier transformation of length M = 2N:<maths id="math0009" num=""><img file="EP1538749A2_D0009.tif" /></maths>

0040As equation (6) shows, the weighting factors are g_i real-valued and symmetrical. Therefore, the result of the transformation, ie the window function w (k), is also real-valued since the imaginary part of the discrete Fourier transform of the weighting factors g_i Is zero. This shows that the equivalent discrete cosine transformation can be used instead of a discrete Fourier transformation as well.

0041The phase correction term in equation (8) is dependent on the integer delay value k₀, As already mentioned, it is required that in case g_i= 1, i = 0,1,2, ..., 2N-1 the system is a perfect reconstruction of the input signal x (k), apart from a constant delay k₀, generated. That is, it should apply:<maths id="math0010" num="(9)"><math display="block"><mrow><msub><mrow><mtext>y (k) = x (k - k</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>)</mtext></mrow></math><img file="EP1538749A2_D0010.tif" /></maths>

0042This can be accomplished by using a low pass prototype impulse response of length n for which<maths id="math0011" num="(10a)"><math display="block"><mrow><mtext>n = L · 2N; L∈ {1,2, ...}</mtext></mrow></math><img file="EP1538749A2_D0011.tif" /></maths> applies. Ie. the low-pass prototype impulse response should have a length n equal to twice the number N of band-pass filters of a reference filter bank equivalent to the time-domain filter or a whole multiple thereof.

0043In addition, the phase parameter k₀ the condition<maths id="math0012" num="(10b)"><math display="block"><mrow><msub><mrow><mtext>k</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext> = λ · N; λ = constant ∈ {1,2,3, ...}</mtext></mrow></math><img file="EP1538749A2_D0012.tif" /></maths> fulfill. In this case, the phase correction term can be written very simplified in equation (8):<maths id="math0013" num=""><img file="EP1538749A2_D0013.tif" /></maths>

0044In this case we obtain for the window function w (k):<maths id="math0014" num=""><img file="EP1538749A2_D0014.tif" /></maths>

0045In order to achieve a perfect reconstruction of the input signal, the low-pass prototype impulse response h (k) must satisfy the following conditions:<maths id="math0015" num=""><img file="EP1538749A2_D0015.tif" /></maths>

0046That is, the low-pass prototype impulse response h (k) at a particular first time which corresponds to the constant delay value k₀ corresponds to the low-pass prototype impulse response that must have the function value "1". At certain further equidistant times spaced from said first value by a value corresponding to the length M = 2N of the prototype low-pass impulse response, the impulse response h (k) must have the function value "0". The remaining function values ​​of the low-pass prototype impulse response h (k) can then be arbitrarily chosen to satisfy the spectral resolution requirements.

0047It should be noted that the total delay of the perfect reconstruction system is k₀ even if h (k) is a non-linear phase filter. In the case of a prototype impulse response h (k) with a linear phase, ie with n = L · 2N and k₀= L · N, has the total delay according to equation (6) for arbitrary real-valued weighting coefficients g_i also the value k₀.

0048In the case of the realization of the equivalent time domain filter 2 shown in FIG. 5, constant delay elements 4 are used in each case, which delay the signal by exactly one sampling period T. In this case, the equivalent time domain filter 2 has a uniform frequency resolution. However, in some applications it is advantageous to use an equivalent time domain filter 2 with a non-uniform frequency resolution. For example, it is possible by an uneven spectral resolution to adapt the signal to human hearing by z. B. at low frequencies narrow filters are used and at high frequencies wider filters.

0049One well-known technique for achieving nonuniform frequency distortion in digital filters is to replace the delay elements with first order all-pass filters, ie delay elements having a so-called all-pass transfer function (eg AG Constantinides: Frequency Transformations for Digital Filters Electronic Letters, 3 (11), 487-489, 1967; W. Schuessler, W. Winkelnkemper: Variable Digital Filters, AECH, 24, 524-525, 1970). This method is used, for example, to develop and implement variable digital filters. Thus, in this way, a certain low pass with a certain cutoff frequency Ω_c from a prototype low-pass filter with a cutoff frequency Ω₀ to be generated. Another application of this distortion technique is to construct so-called short-term spectral analyzes with non-uniform spectral resolution by means of discrete Fourier transformation or with the aid of discrete filter banks.

0050In the present case, this transformation technique is used to achieve uneven frequency resolution within the equivalent time domain filter 2. This is shown in FIG. The structure according to FIG. 6 differs from the structure according to FIG. 5 only in that, instead of the delay stages 4 with uniform frequency resolution, delay stages 5 with an all-pass transfer function are now used.

0051The effect of this measure is illustrated particularly well when considering the transfer functions of the original bandpass impulse responses of the reference filter bank according to FIG. 1, which result from the z-transformation:<maths id="math0016" num=""><img file="EP1538749A2_D0016.tif" /></maths>

0052If in equation (13a) the delay elements z^-k through all-pass transfer functions H_A(z) replaced, we obtain the transfer functions:<maths id="math0017" num=""><img file="EP1538749A2_D0017.tif" /></maths>

0053It is, for example<maths id="math0018" num="(14a)"><math display="block"><mrow><msub><mrow><mtext>H</mtext></mrow><mrow><mtext>A</mtext></mrow></msub><mtext>(Z) =</mtext><mfrac><mrow><msup><mrow><mtext>z</mtext></mrow><mrow><mtext>-1</mtext></mrow></msup><mtext> - a</mtext></mrow><mrow><msup><mrow><mtext>1-a * z</mtext></mrow><mrow><mtext>-1</mtext></mrow></msup></mrow></mfrac><mtext> ; -1≤a≤ + 1</mtext></mrow></math><img file="EP1538749A2_D0018.tif" /></maths>

0054From equation (14a) it can be seen that when the variable a = 0 is inserted, the all-pass transfer function H_A(z) the value z^-1 assumes, ie the construction according to FIG. 6 then corresponds to the construction according to FIG.

0055Since the amount of the frequency response of all-pass delay elements according to the equation<maths id="math0019" num="(14b)"><math display="block"><mrow><msub><mrow><mtext>H</mtext></mrow><mrow><mtext>A</mtext></mrow></msub><msup><mrow><mtext>(e</mtext></mrow><mrow><mtext>jΩ</mtext></mrow></msup><msup><mrow><mtext>) = 1 · e</mtext></mrow><mrow><mtext>j</mtext></mrow></msup><msup><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">φ</mtext></mrow></msup><msup><mrow><mtext>​</mtext></mrow><mrow><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>A</mtext></mrow></msub><mtext>(Ω)</mtext></mrow></msup></mrow></math><img file="EP1538749A2_D0019.tif" /></maths>

0056is constant, the use of the all-pass elements makes the frequency axis corresponding to the phase characteristic of the all-pass elements according to the equation<maths id="math0020" num=""><img file="EP1538749A2_D0020.tif" /></maths> distorted.

0057This frequency distortion characteristic is shown in Figure 7 for some values ​​of the variable a. Plotted in it is the transformed normalized frequency Ω^t above the normalized original frequency Ω. The normalization was carried out in each case so that half the sampling frequency, for example, in a GSM mobile device 4 kHz, the value π corresponds.

0058When this frequency distortion is applied to a reference filter bank as shown in Fig. 1, each of the separate bandpass filters of the reference filter bank is individually according to the equation<maths id="math0021" num=""><img file="EP1538749A2_D0021.tif" /></maths> transformed.

0059An example of this is shown in FIG. In this case, the middle graph shows a representation analogous to FIG. 7, ie, it is the transformed normalized frequency Ω herein^t plotted over the original frequency Ω. Examples are here on the one hand, the special case a = 0, in which the all-pass elements in the pure delay elements z^-1 go over, and on the other hand, the variable a = 0.5 selected.

0060To the left of this graph are the original frequency responses of various bandpass filters of the reference filter bank, here for the first low pass with the impulse response h₀, for the bandpasses with the impulse responses h₄, H₈, H₁₂ as well as for the high pass with the impulse response h₁₆ shown. It is edgewise, ie rotated by 90 °, each applied the attenuation above the normalized frequency Ω.

0061The middle graph shows the frequency responses of these bandpasses which have been transformed due to the uneven frequency resolution, the attenuation also being plotted against the normalized original frequency Ω. In the special case a = 0, the original frequency responses would remain unchanged. For the further illustrated case a = 0.5 results in the frequency response distribution shown in the lower diagram, in which the frequency responses of the low-pass and the lower bandpasses, ie the bandpasses with lower center frequency, become narrowband and the frequency responses of the high passes or bandpasses with higher center frequency broadband.

0062The same effect is achieved when in the equivalent time domain filter according to FIG. 8 the all-pass transfer elements H_A(z) can be used as delay stages 5. This is due to the fact that the total frequency response of the structure according to FIG. 6 corresponds exactly to the bandpass frequency response of the reference system according to FIG. 1, because each of the bandpass filters according to FIG. 1 is transformed according to equation 13b. It should be noted that the originally time-limited impulse response of the system is converted into a recursive impulse response.

0063FIG. 9 shows how a very good adaptation of the frequency characteristic of the input signal to the human ear can be achieved with the aid of this technology in a filter system according to the invention. In this graph, the Bark scale is mapped to the frequency scale. The aurally accurate frequency resolution according to the sound resolution in the form of the center frequencies of the bark frequency ranges (asterisks) in the range 0 to 8 kHz is shown. The solid line shows as comparison the (theoretical) transformation curve of a filter according to the invention with the parameters N + 1 = 21 (<i>M</i>= 40) and using delay stages with all pass transfer functions with a = 0.565.

0064As already mentioned, the weighting factors, ie the function values ​​of the window function w (k), can in principle be constant in order to achieve a fixed filter characteristic. However, to build an adaptive filter, for example, to improve a noisy signal or to achieve any other adaptive spectral range based filtering, this window function w (k) must be variable. As a representative example, adaptive filtering for the purpose of noise suppression will now be described, without limitation of the invention.

0065As described above, the conventional spectral subtraction for noise suppression is based on a short-term spectral analysis and subsequent synthesis using the Discrete Fourier Transform. The parameters required for the Discrete Fourier Transformation or Inverse Discrete Fourier Transformation used for this, such. B. the transformation or Block length M, the window function and the block overlap, must be selected so that on the one hand the requirements for a signal reconstruction without aliasing effect are achieved and on the other hand the desired calculations of the weighting factors are possible.

0066The adaptive weighting factors g_i are determined according to a "spectral subtraction rule". This rule is based either on the periodicity of the input signal or on the short-term energies of the subband signals. Therefore, it is common for the weighting factor calculations to have analytical subband signals and complex bandpass impulse responses ĥ_i(k) introduce:<maths id="math0022" num="(16)"><math display="block"><mrow><msub><mrow><mover accent="true"><mrow><mtext>H</mtext></mrow><mo></mo></mover></mrow><mrow><mtext>i</mtext></mrow></msub><mtext> (k) = h (k) · e </mtext><msup><mrow><mtext>​</mtext></mrow><mrow><mtext>± j</mtext><mfrac><mrow><mtext>2π</mtext></mrow><mrow><mtext>2N</mtext></mrow></mfrac><msub><mrow><mtext>i (kk</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><mtext>)</mtext></mrow></msup><mtext> I = 0,1, ..., 2N-1</mtext></mrow></math><img file="EP1538749A2_D0022.tif" /></maths>

0067The complex subband samples<maths id="math0023" num=""><img file="EP1538749A2_D0023.tif" /></maths> are calculated at specific time steps k ', which are determined solely on the basis of the requirements for the weighting factor calculation, but taking into account the reduced bandwidths of the envelope of the subband signals.

0068The third row of equation (17), apart from the upper sum limit n-1, looks exactly like the IDFT / DFT expression of the time-reversed input signal x (k) multiplied by the prototype low-pass impulse response h (k). The impulse response is used as the effective window for selecting the samples for a signal block<maths id="math0024" num="(18)"><math display="block"><mrow><mtext>x (k '), x (k'-1), x (k'-2), .... x (k'-n + 1)</mtext></mrow></math><img file="EP1538749A2_D0024.tif" /></maths> considered.

0069Without loss of generality, the special case n = 2N can be considered below. Since the weighting factors g_i are calculated as functions of the short-term energies calculated on the basis of the magnitude of the samples or the envelope of the sub-bands, the +/- sign in the last line of equation (17) is not relevant. The magnitude of the samples can thus be determined by a Discrete Fourier Transform or Fast Fourier Transform according to the equation<maths id="math0025" num=""><img file="EP1538749A2_D0025.tif" /></maths> be calculated.

0070A realization of this concept in a window function calculation device 3 is shown schematically in FIG. The signal block of the input signal x (k) for the discrete Fourier transformation is determined here by means of a memory and pre-processing chain 13. Therein, the input signal x (k) is again shifted with delay elements 14 by one sample. Ie. the window function calculation device 3 here has a delay chain, which corresponds to the delay chain in the equivalent time domain filter itself. Thus, in the embodiment shown in Fig. 10, a window function calculator 3 for an equivalent time-domain filter 2 having a uniform frequency resolution is shown. For a filter with non-uniform frequency resolution, a memory chain according to FIG. 6 could also be selected here again.

0071The signal values ​​x (k), k = 0, ..., 2N-1 of this signal block are then multiplied by the corresponding function value of the prototype low-pass impulse response h (k) and then to the 2N inputs of a time / spectral transformation device 10 given. The input signals of the window function calculator 3 and the time / spectral transformation means 10 are consequently the weighted state variables of the time domain filter 2. In this device, 2N output signals are generated therefrom by means of the Discrete Fourier Transformation or Fast Fourier Transformation <img file="EP1538749A2_D0026.tif" />_i(k '), i = 0,1, ..., 2N-1 generated in the spectral range. These are then fed to the weighting coefficient calculator 11 which, for example in the usual way (ie as in the known analysis-synthesis systems) the weighting factors g_i, i = 0, ..., 2N-1 generated. These weighting factors g_i are then passed on to a spectral time transformation device 12, which by corresponding inverse discrete Fourier transform (or inverse fast Fourier transform) the weighting coefficients g_i transformed into the time domain, where the desired window function w (k) arises.

0072For cases where the length of the low-pass prototype impulse response h (k) in the time domain filter 2 is less than the transform length 2N in the weighting coefficient calculator, the signal blocks can be extended to the length of the discrete Fourier transform simply by zero-filling ,

0073This is different in cases where the prototype low-pass impulse response is longer than the transform length 2N, for example, the length n = L * 2N. In these cases, a windowed signal block of length n can be decomposed into modified sequences u (k ', μ) of the transformation length 2N by means of a so-called polyphase preprocessing. (eg P. Vary, U. Heute, W. Hess: Digital Speech Signal Processing; Teubner Verlag 1998, p. 107-110) For this, the sum in equation (17) must be replaced by the substitution<maths id="math0026" num="(20)"><math display="block"><mrow><mtext>κ = ν · 2N + μ; ν = 0,1, ..., L-1; μ = 0,1, ..., 2N-1</mtext></mrow></math><img file="EP1538749A2_D0027.tif" /></maths> in a double sum accordingly<maths id="math0027" num=""><img file="EP1538749A2_D0028.tif" /></maths> be disassembled. The final result is then a Discrete Fourier Transform of the new sequence u (k ', μ), which is ultimately a superposition of adjacent segments of length 2N of weighted signal samples.

0074For the concrete example M = 2N = 4 and n = 8, this is shown in FIG. Here, the time / spectral transformation device 10 can only perform a discrete Fourier transformation of length M = 4. Accordingly, the time / spectral transformation device 10 has only four inputs. On the other hand, signal sections of length 8 must be processed. Therefore, here the memory and preprocessing chain 15 is constructed such that the fifth input value x (4) * h (4) at the first input of the time-spectral transformation device 10 is superposed with the first input value x (0) * h (0) and the sixth input value x (5) * h (5) with the second input value x (1) * h (1), etc. This shows that it is readily possible to construct filter lengths that are larger than the transformation used. Such a construction saves a considerable effort in the coefficient calculation, which in turn shortens the calculation times.

0075It should be noted that the discrete Fourier transform in Figures 10 and 11 is used to obtain values ​​for the real and imaginary parts of the analytical subband signals. The real part is identical to the subband signals y_i of the reference system at the sub-sampled time steps k ', where the imaginary part is an approximation of the Hilbert transformation ŷ_i of the real part is. Therefore:<maths id="math0028" num=""><img file="EP1538749A2_D0029.tif" /></maths>

0076As with the usual spectral subtraction rules (eg Y. Ephraim, D. Malah: Speech Enhancement using a Minimum Mean-Square Error Short Time Spectral Amplitude Estimator, IEEE Transactions Acoustics, Speech, and Signal Processing, Vol. 32, no -1121, December 1984). For example, the weighting factors may each be calculated as the square of the magnitude of the subband signal values:<maths id="math0029" num=""><img file="EP1538749A2_D0030.tif" /></maths>

0077Due to the averaging process that is inherently performed in the corresponding calculation, corresponding weighting factors may be determined according to<maths id="math0030" num=""><img file="EP1538749A2_D0031.tif" /></maths> calculated solely as a function of the real part. Therefore, the complex-valued discrete Fourier transforms in Figures 10 and 11 can also be replaced by the corresponding real-valued discrete cosine transforms.

0078The filter structure according to the invention thus makes it possible in a simple manner to produce any desired spectral signal modifications with uniform or non-uniform spectral resolution and with fixed or adaptive weighting factors of the subband signals. The desired behavior is achieved solely with a single equivalent time domain filter with an impulse response, which is the product of a prototype low-pass impulse response with an optionally time variant window function is. The weighting factors can preferably be calculated with a reduced clock rate within the frequency band ranges using Discrete Fourier Transformation or Discrete Cosine Transform of the weighted state variables of the time domain filter. This is a very significant advantage since the conditions for the signal reconstruction such as the spectral resolution, the delay or aliasing effects as well as the weighting factor calculation, ie the temporal resolution are decoupled.

0079The (partial) filter systems shown schematically in the figures can basically be realized in the form of discrete circuit structures. However, implementation is particularly preferably carried out by means of software-programmed signal processors or in the form of ASCIs. Such a construction is considerably less expensive. In addition, such a realization is also space-saving and has no disadvantages compared to a discrete circuit structure.

0080Finally, it is once again pointed out that the methods and filter constructions specifically illustrated in the figures and described above are exemplary embodiments which can be modified by the person skilled in the art without departing from the scope of the invention. So z. B. an adaptive filter may also be implemented such that the input values ​​for the weighting factor calculator are taken at the output of the delay chain of the equivalent time domain filter. Thus, a separate delay chain could be saved for the weighting factor calculation device.