Circuit and method for adaptive suppression of acoustic feedback

0001The present invention relates to a circuit and a method for adaptively suppressing acoustic feedback in accordance with the preambles of the independent claims. It is used, for example, in digital hearing aids.

0002In acoustic systems with a microphone, a loudspeaker or handset and an electronic signal processing part in between, there can be acoustic feedback between the loudspeaker or handset on the one hand and the microphone on the other hand. The acoustic feedback causes undesirable distortions and, in extreme cases, leads to unstable behavior of the system, for example an unpleasant whistling. Since the unstable operation is unacceptable, the signal amplification of the signal processing part often has to be set lower than effectively desired.

0003The suppression of acoustic feedback in digital hearing aids can basically be approached with different approaches. The best results are currently achieved with the adaptive filtering method.

0004Various systems with adaptive filtering are known. Basically, an acoustic input signal is recorded in such systems and converted into a digital electrical signal. An echo estimate is subtracted from this. The echo-compensated signal is transformed with a necessary hearing correction into a digital output signal, converted into an analog electrical signal and emitted as an acoustic output signal. On its way back to the microphone, the acoustic signal is deformed according to a feedback characteristic and is superimposed on an external acoustic signal to form a new acoustic input signal. To calculate the echo estimate, the fixed delays contained in the system are modeled and the unknown feedback characteristic is modeled.

0005Unfortunately, such well-known systems with adaptive filtering are not sufficient to achieve low-distortion transmission in a realistic environment with satisfactory convergence management. The difficulty stems from the fact that real signals such as speech or music have an autocorrelation function that cannot be neglected. The adaptive filter interprets the autocorrelation of the signal to a certain extent as a feedback effect and the result is a partial cancellation of the desired signal. This effect is most extreme with purely periodic signals (e.g. alarm tones). The system can be improved if the feedback characteristic is modeled using decorrelated signals. There are different approaches to this, which are explained below.

0006A first approach involves the use of an artificial noise signal. Such a system is known, for example, from European patent applications EP-415 677, EP-634 084 and EP-671 114 from GN Danavox AS. The common property of such systems is the use of an artificial noise signal to decorrelate the signals. The noise signal is either switched on instead of the output signal when required or is continuously added to the output signal. The disadvantage of these systems is the effort required to control the noise signal power in such a way that the noise remains as inaudible as possible and nevertheless a sufficiently good convergence speed can be achieved.

0007A second approach involves the use of fixed orthogonal transformations. Such a system from Phonak AG was published, for example, as a European patent application EP-585 976. The common property of such systems is the use of fixed orthogonal transformations for decorrelation of the signals. With these systems, the filtering and updating of the coefficients is not carried out directly in the time domain. The disadvantage of these systems, in addition to the generally greater computing effort, is the additional delay in the signal processing path caused by block-by-block processing.

0008A third approach involves the use of adaptive decorrelation filters. Such a system has been described, for example, in Mamadou Mboup et al., "Coupled Adaptive Prediction and System Identification: A Statistical Model and Transient Analysis '', Proc. 1992 IEEE ICASSP, 4; 1-4, 1992 feasible systems differ in the different arrangement and implementation of the decorrelation filter. The disadvantage of the published system is the use of relatively slow transversal filter decorrelators, which due to their structure cannot adapt very quickly to the changing statistical properties of their input signals. The coefficients of the two decorrelation filters are generally determined by decorrelation of the output signal reaching the loudspeaker or listener. This is to make the speed of convergence independent of frequency. There is therefore no special weighting of the frequencies with high gains in the signal processing path, which are particularly critical for the feedback behavior.

0009It is an object of the invention to provide a circuit and a method for adaptive suppression of acoustic feedback which do not have the disadvantages of the known systems. In particular, an optimal convergence behavior with minimal, inaudible distortions and without additional signal delay should be achieved with the least possible effort.

0010The object is achieved by the circuit and the method as defined in the independent patent claims.

0011The present invention belongs to the group of systems with adaptive decorrelation filters. It takes advantage of the knowledge that cross-link filter structures are particularly suitable for fast decorrelation. Such cross-link filter structures are known from speech signal processing and are used there for linear prediction. Algorithms for the decorrelation of a signal using a cross-link filter are known and can be found in the specialist literature, for example. with S. Thomas Alexander, "Adaptive Signal Processing", Springer-Verlag New York, 1986.

0012The present invention models the feedback path and adaptively follows its changes over time by means of an optimized tracking. The feedback signal components are continuously removed from the input signal. This significantly increases the signal gain permitted for stable operation. This enables the use of higher amplifications (e.g. in the case of severe hearing impairment) or a more pleasant open care (e.g. in the case of minor hearing loss).

0013The circuit according to the invention is used in an acoustic system with at least one microphone for generating an electrical input signal, at least one loudspeaker or receiver and an electronic signal processing part located in between. It contains a filter for modeling a feedback characteristic, an update unit for calculating current coefficients for the filter, a subtractor for calculating an echo-compensated input signal by subtracting an echo estimate supplied by the filter from a digital input signal, a delay element for calculating a delayed output signal and two adaptive cross-link correlation filter. A first cross-link decorrelation filter is arranged for decorrelation of the echo-compensated input signal, and a second cross-link decorrelation filter is arranged for decorrelation of the delayed output signal by means of coefficients originating from the first cross-link decorrelation filter. The two cross-link decorrelation filters are configured to calculate their cross-link coefficients by means of adaptive decorrelation of the echo-compensated input signal.

0014The first decorrelation filter, a cross-link decorrelator, extracts the noise-like components it contains from the echo-compensated signal. In parallel, the delayed output signal is converted into a transformed signal in the second decorrelation filter, a cross-link filter, using the coefficients originating from the cross-link decorrelator. The special feature of this arrangement is that the cross-link decorrelator and the cross-link filter are exchanged in comparison with the conventional arrangement, in which the delayed output signal is decorrelated rather than the echo-compensated signal. The circuit according to the invention has the great advantage that the spectral maxima present in the hearing correction are retained in the transformed signal. These maxima mostly correspond to the most critical frequencies for the feedback, and these should be taken into account with the correspondingly large weighting when updating the filter coefficients.

0015In the method according to the invention for adaptive suppression of acoustic feedback, an electrical input signal is generated with at least one microphone, a feedback characteristic is modeled with a filter, current coefficients for the filter are calculated with an update unit, an echo-compensated input signal is generated with a subtractor by subtracting one supplied by the filter Echo estimate calculated from a digital input signal, and a delayed output signal is calculated with a delay element. The echo-compensated input signal is decorrelated with a first cross-link decorrelation filter, and the delayed output signal is decorrelated with a second cross-link decorrelation filter by means of coefficients originating from the first cross-link decorrelation filter. The cross-link coefficients of the two cross-link decorrelation filters are calculated by means of adaptive decorrelation of the echo-compensated input signal.

0016The present invention differs significantly from all previously published systems for suppressing acoustic feedback. New are the special arrangement and implementation of the blocks for the decorrelation and standardization, the control of the forgetting factor and the step size factor, as well as the possibility of staggered updating in the combination according to the invention. The present invention permits maximum convergence speeds with minimal distortions, since the filter coefficients are updated in terms of time and frequency mainly where the large amplifications occur in the hearing correction.

0017In the following the invention and for comparison also the prior art will be described in detail with reference to figures. The block diagrams show:<dl id="dl0001"><dt>Fig. 1</dt><dd>a general system for adaptive suppression of acoustic feedback according to the prior art,</dd><dt>Fig. 2</dt><dd>a system using a noise signal according to the prior art,</dd><dt>Fig. 3</dt><dd>a system using orthogonal transformations according to the prior art,</dd><dt>Fig. 4</dt><dd>a system using adaptive decorrelation filters according to the prior art,</dd><dt>Fig. 5</dt><dd>the system according to the invention,</dd><dt>Fig. 6</dt><dd>2 shows a detailed drawing of a delay element of the system according to the invention,</dd><dt>Fig. 7</dt><dd>2 shows a detailed drawing of a filter of the system according to the invention,</dd><dt>Fig. 8</dt><dd>2 shows a detailed drawing of an update unit of the system according to the invention,</dd><dt>Fig. 9</dt><dd>1 a detailed drawing of a standardization unit of the system according to the invention,</dd><dt>Fig. 10</dt><dd>1 shows a detailed drawing of a speed control unit of the system according to the invention,</dd><dt>Figure 11</dt><dd>2 shows a detailed drawing of a cross-link decorrelator of the system according to the invention,</dd><dt>Fig. 12</dt><dd>a detailed drawing of a cross-link filter of the system according to the invention and</dd><dt>Fig. 13</dt><dd>a detailed drawing of a control unit of the system according to the invention.</dd></dl>

0018A generally known system for adaptive suppression of acoustic feedback is in <b>Figure 1</b> shown. An acoustic input signal a_in(t) is picked up by a microphone 1 and initially converted into an electrical signal d (t). A subsequent AD converter 2 determines a digital input signal d therefrom_n, Of these, an echo estimate y is made in a subtractor 3_n deducted. The echo-compensated signal e_n is converted into a digital output signal with a correction 4 that can be adapted to the respective application, for example an individual hearing correction for a hearing impaired person_n transformed. The DA converter 5 carries out a conversion into an electrical signal u (t), which is transmitted via a loudspeaker or receiver 6 as an acoustic output signal a_out(t) is emitted. The acoustic output signal a_out(t) is deformed on its way back to the microphone 1 according to a feedback characteristic 7 characterized by an impulse response h (t) into a signal y (t) and is superimposed on an external acoustic signal s (t) (8). The remaining components in the system are a delay element 9, a filter 10 and an update unit 11. The delay element 9 simulates the fixed delays contained in the system, as a result of which a delayed signal x_n arises. The filter 10 models the unknown feedback characteristic. The current coefficients are continuously updated in the update unit 11<u>w</u>_n calculated for the filter. A variant of the LMS algorithm (Least Mean Square) is usually used.

0019The generally known system is not sufficient because of the not negligible autocorrelation function of real acoustic signals s (t) in order to achieve a low-distortion transmission in a realistic environment with a satisfactory convergence behavior. The system can be improved if the update unit works with decorrelated signals.

0020<b>Figure 2</b> shows a system which uses an artificial noise signal to decorrelate the signals. Such a system is known, for example, from European patent applications EP-415 677, EP-634 084 and EP-671 114 from GN Danavox AS. The artificial noise signal is generated in a noise generator 17 and u. Via a power control unit 18 to the digital output signal_n added (19). The artificial noise signal is also fed to the update unit 11 via a delay element 20. The noise signal is either only when needed instead of the output signal u_n switched on or running to the output signal u_n added.

0021<b>Figure 3</b> shows a system that uses fixed orthogonal transformations to decorrelate the signals. Such a system from Phonak AG was published, for example, as a European patent application EP-585 976. The echo-compensated signal e_n and the output signal u_n are transformed into the frequency range via transformation units 21 and 22 or the echo estimate y_n is recovered via an inverse transformation 23. With these systems, the filtering and updating of the coefficients is not carried out directly in the time domain.

0022<b>Figure 4</b> shows a system which uses adaptive decorrelation filters 12, 13 for decorrelation of the signals. Such a system has been described, for example, in Mamadou Mboup et al., "Coupled Adaptive Prediction and System Identification: A Statistical Model and Transient Analysis", Proc. 1992 IEEE ICASSP, 4; 1-4, 1992. The echo-compensated signal e_n and the delayed output signal x_n are decorrelated by the adaptive decorrelation filters 12, 13. The coefficients<u>a</u>_n of the two decorrelation filters 12, 13 are determined in block 13 by means of decorrelation of the delayed output signal x_n calculated.

0023An embodiment of a system according to the invention is shown in <b>Figure 5</b> shown. In addition to the blocks 1 to 11 described above, the system according to the invention uses adaptive cross-link decorrelation filters, namely a cross-link decorrelator 12 and a cross-link filter 13 running in parallel therewith. The cross-link filter structures known from speech signal processing have proven to be particularly suitable for fast decorrelation , They are used there for linear prediction. Algorithms for the decorrelation of a signal using a cross-link filter are known.

0024The cross-link decorrelator 12 extracts from the echo-compensated signal e_n Noise-like components contained therein e^M_n, In parallel, in the cross-link filter 13 with coefficients originating from the cross-link decorrelator 12<u>k</u>_n the delayed output signal x_n into a transformed signal x^M_n converted. The special feature of this arrangement is the interchanging of the two adaptive decorrelation filters 12 and 13 compared to the usual procedure, in which the echo-compensated signal e_n, but the delayed signal x_n is decorrelated. However, the arrangement according to the invention has the great advantage that the spectral maxima present in the hearing correction 4 in the transformed signal x^M_n remain. These maxima mostly correspond to the most critical frequencies for the feedback, and these should be used when updating the filter coefficients<u>w</u>_n are taken into account with the correspondingly large weighting.

0025The order of the two cross slide decorrelation filters 12, 13 is determined from a compromise between the desired degree of decorrelation and the computational effort involved. For the special case of filters of the second order (M = 2), an upper limitation of the second cross-link coefficient k_2n again achieved a significant improvement in system behavior. This upper limitation of the second cross-link coefficient means that pure sine tones are not completely decorrelated. This in turn has the great advantage that the whistling tones that occur during unstable operation are compensated for much more quickly.

0026Furthermore, the system according to the invention contains a control unit 14. The control unit 14 continuously compares the power of the input signal d_n with the power of the echo-compensated signal e_n, The ratio of the two services determines which forgetting factor λ_n is used in the update unit 11. If the power of the echo-compensated signal is greater than the power of the input signal, this is almost always an indication that the echo estimate y_n and thus the coefficients <u>w</u>_n of the filter 10 are too large in terms of amount. By setting λ_n&lt;1 the coefficients quickly converge to a more suitable value. In normal operation, however, λ_n= 1 set. The described control of the forgetting factor λ_n provides improved convergence behavior with rapid changes in the feedback path. An internal feedback generated temporarily by the system is immediately recognized and quickly adapted to the external feedback path.

0027As a further difference from other systems, the update unit 11 contains a standardization unit 15 and a speed control unit 16. The arrangement of the blocks described below can be seen from FIG. 8, which represents a more precise specification of the update unit 11. The normalization unit 15 enables the NLMS algorithm (Normalized Least Mean Square) to be used. It calculates the power of the signal e^M_n, The special thing about this arrangement is that the standardization regarding e^M_n and not as usual regarding x^M_n he follows. The rate of convergence thus becomes dependent on the ratio of the powers of x^M_n and e^M_n, This ratio is essentially given by the amplification contained in the hearing correction 4. The gain in the hearing correction is not constant in time in the general, non-linear case (e.g. compression method). In the method according to the invention, the convergence behavior of the adaptive filter 10 modeling the feedback characteristic 7 therefore depends on the temporal behavior of the hearing correction 4, ie on the temporal course of its amplification and frequency response. In times of high amplification with particularly critical feedback behavior, the coefficients are quickly adjusted <u>w</u>_n and in times of small amplification with non-critical feedback behavior, a correspondingly slower adaptation takes place. The update takes place mainly in the times when it is actually necessary. This procedure combines rapid convergence in the critical case with almost distortion-free processing in the uncritical case.

0028The speed control unit 16 supplies a step size factor β_n for the NLMS algorithm. The speed control unit 16 supplies values ​​for β_n starting with the standard value β_Max and gradually decreasing to the final value β within the first seconds after starting_min, This procedure allows the filter coefficients to converge very quickly after starting<u>w</u>_n from zero to their setpoints. The resulting initial signal distortion is less severe than the otherwise much longer feedback whistle.

0029The update unit 11 can be carried out in such a way that only a certain small, cyclically changing part of the (N + 1) filter coefficients is updated at each discrete point in time. This considerably reduces the computing effort required. The system does not have to be made slower than it is to prevent audible distortion.

0030A specific embodiment of the present invention is described in more detail below on the basis of FIG. 5. The microphone 1, the AD converter 2, the DA converter 5 and the receiver 6 are assumed to be ideal in the consideration. The characteristics of the real acoustic and electrical transducers can be viewed as part of the feedback characteristic 7. The following relationships apply to the AD converter 2 and the DA converter 5. T and f denote_s the sampling period or sampling frequency and the index n the discrete point in time.<maths id="math0001" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">d</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic"> = d (n * T) u (n * T) = u</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><mtext mathvariant="italic">T =</mtext><mtext> 1/</mtext><msub><mrow><mtext mathvariant="italic">f</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">   f</mtext></mrow><mrow><mtext mathvariant="italic">s</mtext></mrow></msub><mtext mathvariant="italic"> =</mtext><mtext> 16</mtext><mtext mathvariant="italic">kHz</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0001.tif" /></maths>

0031The following relationships apply to the subtractor 3 and the hearing correction 4. The function f () stands for any nonlinear function of its arguments. It results from the selected procedure for correcting individual hearing loss.<maths id="math0002" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic"> = d</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic"> - y</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">u</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic"> = f (e</mtext></mrow><mrow><mtext>0</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext>2</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic">, ..., e</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext mathvariant="italic">)</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0002.tif" /></maths>

0032The acoustic transmission path is modeled using the feedback characteristic 7 and an adder 8. The operator * is to be understood as a convolution operator and h (τ) stands for the impulse response of the feedback. The signal incident from the outside is denoted by s (t).<maths id="math0003" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mtext mathvariant="italic">y (t) =</mtext><msub><mrow><mtext> α</mtext></mrow><mrow><mtext mathvariant="italic">out</mtext></mrow></msub><mtext mathvariant="italic">(D) * h (τ)</mtext></mrow></mtd></mtr><mtr><mtd><mrow><msub><mrow><mtext>α</mtext></mrow><mrow><mtext mathvariant="italic">in</mtext></mrow></msub><mtext mathvariant="italic">(t) = s (t) + y (t)</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0003.tif" /></maths>

0033The delay element 9 is in <b>Figure 6</b> shown, and the following relationships apply. The delay length L must be matched to the sum of the delays of the acoustic and electrical transducers.<maths id="math0004" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">x</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext mathvariant="italic"> = u</mtext></mrow><mrow><mtext mathvariant="italic">nL</mtext></mrow></msub></mrow></mtd></mtr><mtr><mtd><mrow><mtext mathvariant="italic">L</mtext><mtext> = 16...24   (</mtext><mtext mathvariant="italic">L * T</mtext><mtext> = 1</mtext><mtext mathvariant="italic">ms</mtext><mtext>...1.5</mtext><mtext mathvariant="italic">ms</mtext><mtext>)</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0004.tif" /></maths>

0034The filter 10 is in <b>Figure 7</b> shown, and the following relationships apply. Underlined sizes mean the similar elements combined into vectors. The factor r allows a range to be selected so that the filter coefficients are always in the range -1 w w regardless of the hearing correction 4_kn &lt;1 can be kept. The filter order N must be matched to the length of the impulse response h (τ).<maths id="math0005" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">y</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">r</mtext><mtext>·</mtext><munder accentunder="true"><mrow><mtext mathvariant="italic">w</mtext></mrow><mo>̲</mo></munder><msubsup><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">T</mtext></mrow></msubsup><mtext>·</mtext><munder accentunder="true"><mrow><mtext mathvariant="italic">x</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">r</mtext><mtext>·</mtext><apply><sum /><lowlimit><mtext mathvariant="italic">k</mtext><mtext>=0</mtext></lowlimit><uplimit><mtext mathvariant="italic">N</mtext></uplimit><mrow><msub><mrow><mtext mathvariant="italic">w</mtext></mrow><mrow><mtext mathvariant="italic">k, n</mtext></mrow></msub><mtext>·</mtext><msub><mrow><mtext mathvariant="italic">x</mtext></mrow><mrow><mtext mathvariant="italic">nk</mtext></mrow></msub></mrow></apply></mrow></mtd></mtr><mtr><mtd><mrow><mtext>r = 1 / 128.1 / 64.1 / 32.1 / 16.1 / 8.1 / 4.1 / 2.1 / 1</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mtext>N = 32 ... 64 (</mtext><mtext mathvariant="italic">N</mtext><mtext>·</mtext><mtext mathvariant="italic">T</mtext><mtext> = 2</mtext><mtext mathvariant="italic">ms</mtext><mtext>...4</mtext><mtext mathvariant="italic">ms</mtext><mtext>)</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0005.tif" /></maths>

0035The update unit 11 is in <b>Figure 8</b> shown, and the following relationships apply. The formula is in vector notation and element notation.<maths id="math0006" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><munder accentunder="true"><mrow><mtext mathvariant="italic">w</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>+1</mtext></mrow></msub><msub><mrow><mtext> = λ</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext>·</mtext><munder accentunder="true"><mrow><mtext mathvariant="italic">w</mtext></mrow><mo>̲</mo></munder><msub><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext>+ β</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext>·</mtext><mfrac><mrow><msubsup><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">M</mtext></mrow></msubsup></mrow><mrow><msub><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub></mrow></mfrac><mtext>·</mtext><munder accentunder="true"><mrow><mtext mathvariant="italic">x</mtext></mrow><mo>̲</mo></munder><msubsup><mrow><mtext>​</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">M</mtext></mrow></msubsup></mrow></mtd></mtr><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">w</mtext></mrow><mrow><mtext mathvariant="italic">k, n</mtext></mrow></msub><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>+1</mtext></mrow></msub><msub><mrow><mtext> = λ</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext>·</mtext><msub><mrow><mtext mathvariant="italic">w</mtext></mrow><mrow><mtext mathvariant="italic">k, n</mtext></mrow></msub><msub><mrow><mtext>+ β</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext>·</mtext><mfrac><mrow><msubsup><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">M</mtext></mrow></msubsup></mrow><mrow><msub><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub></mrow></mfrac><mtext>·</mtext><msubsup><mrow><mtext mathvariant="italic">x</mtext></mrow><mrow><mtext mathvariant="italic">nk</mtext></mrow><mrow><mtext mathvariant="italic">M</mtext></mrow></msubsup><mtext mathvariant="italic">   </mtext><mtext>(0 ≤ </mtext><mtext mathvariant="italic">k</mtext><mtext> ≤ </mtext><mtext mathvariant="italic">N</mtext><mtext>)</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0006.tif" /></maths>

0036In the preferred embodiment, not all (N + 1) filter coefficients are updated at the same time, but only K. The following relationships apply assuming that K is an integer divisor of (N + 1). The variable c_n is used as a counter variable.<maths id="math0007" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mtext mathvariant="italic">k</mtext><mtext> = </mtext><mtext mathvariant="italic">K</mtext><mtext>· int</mtext><mfenced open="(" close=")"><mrow><mfrac><mrow><msub><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mrow><mtext mathvariant="italic">K</mtext></mrow></mfrac></mrow></mfenced><mtext>,...,</mtext><mtext mathvariant="italic">K</mtext><mtext>· int</mtext><mfenced open="(" close=")"><mrow><mfrac><mrow><msub><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>-1</mtext></mrow></msub></mrow><mrow><mtext mathvariant="italic">K</mtext></mrow></mfrac></mrow></mfenced><mtext>+</mtext><mtext mathvariant="italic">K</mtext><mtext>-1</mtext></mrow></mtd></mtr><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext> = (</mtext><msub><mrow><mtext mathvariant="italic">c</mtext></mrow><mrow><mtext mathvariant="italic">n-1</mtext></mrow></msub><mtext>+2) mod (</mtext><mtext mathvariant="italic">N</mtext><mtext>+1)</mtext></mrow></mtd></mtr><mtr><mtd><mrow><mtext mathvariant="italic">N</mtext><mtext> = 47   </mtext><mtext mathvariant="italic">K</mtext><mtext> = 4</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0007.tif" /></maths>

0037The updating unit 11 in turn contains the normalization unit 15 and the speed control unit 16. The normalization unit 15 is shown in FIG <b>Figure 9</b> shown, and the following relationships apply. The coefficients g and h determine the length of the time interval over which an averaging of the power of e^M_n takes place.<maths id="math0008" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">G</mtext><mtext>·</mtext><msub><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">n-</mtext></mrow></msub><msub><mrow><mtext>​</mtext></mrow><mrow><mtext>1</mtext></mrow></msub><mtext>+</mtext><mtext mathvariant="italic">H</mtext><mtext>·(</mtext><msubsup><mrow><mtext mathvariant="italic">e</mtext></mrow><mrow><mtext mathvariant="italic">n</mtext></mrow><mrow><mtext mathvariant="italic">M</mtext></mrow></msubsup><msup><mrow><mtext>)</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></mrow></mtd></mtr><mtr><mtd><mrow><mtext mathvariant="italic">G</mtext><mtext> = 63/64   </mtext><mtext mathvariant="italic">H</mtext><mtext> = 1-</mtext><mtext mathvariant="italic">G</mtext><mtext> = 1/64</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0008.tif" /></maths>

0038The speed control unit 16 is in <b>Figure 10</b> shown, and the following relationships apply. The step size factor β_n is based on β_Max gradually reduced by a factor of 0.5 to β_min, The optimal values ​​for β_Max and ß_min depend on the individual hearing correction ( 4). The variable c_n is used as a counter variable.<maths id="math0009" num=""><img file="EP0930801A2_D0009.tif" /></maths>

0039The cross-link decorrelator 12 is in <b>Figure 11</b> shown, and the following relationships apply. In addition to the recursion formulas for the calculation of eⁱ_n and bⁱ_n the sizes dⁱ_n and nⁱ_n are determined for the tracking of the coefficients k_in, The filter order M results from a compromise between the desired degree of decorrelation and the required computing effort.<maths id="math0010" num=""><img file="EP0930801A2_D0010.tif" /></maths>

0040In the preferred embodiment with filter order M = 2, complete decorrelation is achieved by limiting the second coefficient k_2n prevented. The following relationships apply.<maths id="math0011" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext>2,</mtext><mtext mathvariant="italic">n</mtext></mrow></msub><mtext> = min (</mtext><msub><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext>2,</mtext><mtext mathvariant="italic">n</mtext></mrow></msub><mtext>,</mtext><msub><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext>)</mtext></mrow></mtd></mtr><mtr><mtd><mrow><msub><mrow><mtext mathvariant="italic">k</mtext></mrow><mrow><mtext>Max</mtext></mrow></msub><mtext> = 0.921875</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0930801A2_D0011.tif" /></maths>

0041The cross member filter 13 is in <b>Figure 12</b> shown, and the following relationships apply.<maths id="math0012" num=""><img file="EP0930801A2_D0012.tif" /></maths>

0042The control unit 14 is in <b>Figure 13</b> shown, and the following relationships apply. The forgetting factor λ_n results from the ratio of the two services n^d_n and n^e_n, There is a hysteresis in the middle area.<maths id="math0013" num=""><img file="EP0930801A2_D0013.tif" /></maths>

0043The preferred embodiment can be easily programmed on a commercially available signal processor or implemented in an integrated circuit. For this, all variables must be appropriately quantized and the operations optimized for the existing architectural blocks. Particular attention is paid to the treatment of quadratic sizes (services) and division operations. Depending on the target system, there are optimized procedures for this. However, these are not in themselves the subject of the present invention.