Abstract:
The circuit for adaptive suppression of noise is a component part of a digital-hearing aid, consists of two microphones ( 1, 2 ), two AD—converters ( 3, 4 ), two compensating filters ( 5, 6 ), two retarding elements ( 7, 8 ), two subtractors ( 9, 10 ), a processing unit ( 11 ), a DA—converter ( 13 ), an earphone ( 15 ) as well as the two filters ( 17, 18 ). The method for adaptive suppression of noise can be implemented with the indicated circuit. The two microphones ( 1, 2 ), provide two differing electric signals (d 1 (t), d 2 (t)), which are digitalized in the two AD—converters ( 3, 4 ) and pre-processed together with the two fixed compensation filters ( 5, 6 ). Downstream the compensation filters are arranged the two filters ( 17, 18 ) symmetrically crosswise in a forward direction and having adaptive filter coefficients (w 1 , w 2 ). The filter coefficients (w 1 , w 2 ) are calculated by a stochastic gradient procedure and updated in real time while minimizing a quadratic cost function consisting of cross-correlation terms. As a result of this, spectral differences of the input signals are selectively amplified. With a suitable positioning of the microphones ( 1, 2 ) or selection of the directional characteristics, the signal to noise ratio of output signals (s 1 , s 2 ) compared to that of the individual microphone signals (d 1 (t), d 2 (t)) can be significantly increased. Preferably, one of the two improved output signals (s 1 , s 2 ) within one of the processing units ( 11, 12 ) is subjected to the usual processing specific to hearing aids, sent to one of the DA—converters ( 13, 14 ) and acoustically output once again through one of the earphones ( 15, 16 ). Four additional cross-over element filters ( 19-22 ) carry out a signal-dependent transformation of the input and output signals (y 1 , y 2 ; s 1 , s 2 ), and solely the transformed signals are utilized for the updating of the filter coefficients (w 1 , w 2 ). This makes possible a rapidly reacting, and nonetheless calculation-efficient updating of the filter coefficients (w 1 , w 2 ), and in contrast to other methods only causes minimal audible distortions.

Description:
BACKGROUND OF THE INVENTION 
   The invention presented here concerns a circuit and a method for the adaptive suppression of noise such as may be used in digital hearing aids. 
   The healthy human sense of hearing makes it possible to concentrate on one discussion partner in an acoustic situation, which is disturbed by noise. Many people wearing a hearing aid, however, suffer from a strongly-reduced speech intelligibility, as soon as, in addition to the desired speech signal, interfering background noise is present. 
   Many methods for the suppression of interfering background noise have been suggested. They can be split-up into single channel methods, which require only one input signal, and into multi-channel methods, which by means of several acoustic inputs make use of the spatial information in the acoustic signal. 
   In case of all single channel methods, up until now no relevant improvement of the speech intelligibility could be proven. Solely an improvement of the subjectively perceived signal quality is achieved. In addition, these methods fail in that instance important in practice, in which both the useful—as well as the interfering signals are speech (so-called cocktail party situation). None of the single channel methods is in a position to selectively emphasize an individual speech signal from a mixture. 
   In case of the multi-channel methods for the suppression of noise, one departs from the assumption, that the acoustic source, from which the useful signal is emitted, is situated in front of the listener, while the interfering noise impinges from other directions. This simple assumption proves successful in practice and accommodates the supporting lip-reading. The multi-channel methods can be further subdivided into fixed systems, which have a fixed predefined directional characteristic, and into adaptive systems, which adapt to the momentary noise situation. 
   The fixed systems operate either with the use of directional microphones, which have two acoustic inputs and which provide an output signal dependent on the direction of impingement, or with the use of several microphones, the signals of which are further processed electrically. Manual switching under certain circumstances enables the choice between different directional characteristics. Systems of this type are available on the market and are increasingly also being incorporated into hearing aids. 
   From the adaptive systems under development at the present time one has the hope, that they will optimally suppress interfering noise in dependence of the momentary situation and therefore be superior to the fixed systems. An approach with an adaptive directional microphone was presented in Gary W. Elko and Anh-Tho Nguyen Pong, “A Simple Adaptive First-Order Differential Microphone”, 1995 IEEE ASSP Workshop on Applications of Signal Processing to Audio and Acoustics, New Paltz, N.Y. In that solution, the shape of the directional characteristic is adjusted in function of the signal by means of an adaptive parameter. As a result of this, an individual signal impinging from the side can be suppressed. Due to the limitation to a single adaptive parameter, the system only works in simple sound situations with a single interfering signal. 
   Numerous investigations have been carried out using two microphones, each of which is located at one ear. In the case of these so-called adaptive beam formers, the sum—and the difference signal of the two microphones are utilized as input for an adaptive filter. The foundations for this kind of processing were published by L. J. Griffiths and C. W. Jim, “An Alternative Approach to Linearly Constrained Adaptive Beamforming”, IEEE Transactions on Antennas and Propagation, vol. AP-30 No. 1 pp. 27-34, January 1982. These Griffiths-Jim—beam formers can also operate with more than two microphones. Interfering noises can be successfully suppressed with them. Problems, however, are created by the spatial echoes, which are present in real rooms. In extreme cases this can lead to the situation that, instead of the interfering signals, the useful signal is suppressed or distorted. 
   In the course of the past years, great progress has been made in the field of so-called blind signal separation. A good compilation of the research results to date can be found in Te-Won Lee, “Independent Component Analysis, Theory and Applications”, Kluwer Academic Publishers, Boston, 1998. In it, one departs from an approach, in which M statistically independent source signals are received by N sensors in differing mixing ratios (M and N are natural numbers), whereby the transmission functions from the sources to the sensors are unknown. It is the objective of the blind signal separation to reconstruct the statistically independent source signals from the known sensor signals. This is possible in principle, if the number of sensors N corresponds at least to the number of sources M, i.e., N≧M. A great number of different algorithms have been suggested, whereby most of them are not at all suitable for an efficient processing in real time. 
   Considered as a sub-group can be those algorithms that, instead of the statistical independence, only call for a non-correlation of the reconstructed source signals. These approaches have been comprehensively investigated by Henrik Sahlin, “Blind Signal Separation by Second Order Statistics”, Chalmers University of Technology Technical Report No. 345, Göteborg, Sweden, 1998. 
   He was able to prove, that the requirement of uncorrelated output signals is entirely sufficient for acoustic signals. Thus, for example, the minimization of a quadratic cost function consisting of cross-correlation terms can be carried out with a gradient process. In doing so, filter coefficients are changed step-by-step in the direction of the negative gradient. A process of this type is described in Henrik Sahlin and Holger Broman, “Separation of Real World Signals”, Signal Processing vol. 64 No. 1, pp. 103-113, January 1998. There it is utilized for the noise suppression in a mobile telephone. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to indicate a circuit and a method for the adaptive suppression of noise, which are based on the known systems, which, however, are superior to these in essential characteristics. In particular, with an as small as possible effort an optimum convergence behaviour with minimal, inaudible distortions and without any additional signal delay shall be achieved. 
   The invention presented here belongs to the group of systems for the blind signal separation by means of methods of the second order, i.e., with the objective of achieving uncorrelated output signals. In essence, two microphone signals are separated into useful signal and interfering signals by means of blind signal separation. A consistent characteristic at the output can be achieved, if the signal to noise ratio of a first microphone is always greater than that of a second microphone. This can be achieved either by the first microphone being positioned closer to the useful source than the second microphone, or by the first microphone, in contrast to the second microphone, possessing a directional characteristic aligned to the useful source. 
   The calculation of the de-correlated output signals is carried out with the minimization of a quadratic cost function consisting of cross-correlation terms. To do this, a special stochastic gradient process is derived, in which expectancy values of cross-correlations are replaced by their momentary values. This results in a rapidly reacting and efficient to calculate updating of the filter coefficients. 
   A further difference to the generally known method consists of the fact that, for updating the filter coefficients, signal-dependent transformed versions of the input—and output signals are utilized. The transformation by means of cross-over element filters implements a spectral smoothing, so that the signal powers are distributed more or less uniformly over the frequency spectrum. As a result of this, during the updating of the filter coefficients all spectral components are uniformly weighted, independent of the currently present power distribution. This also for real acoustic signals with not to be neglected auto-correlation functions makes possible a low-distortion processing simultaneously with a satisfactory convergence characteristic. 
   For an optimum functioning of the circuit in accordance with the invention and of the method in accordance with the invention, the microphone inputs can be equalized to one another with compensation filters. A uniform standardizing value for the updating of all filter coefficients is utilized. It is calculated such that in all cases only one of the two filters is adapted with maximum speed, depending on the circumstance of whether at the moment useful signal or interfering noise signals are dominant. This procedure makes possible a correct convergence even in the singular case, in which only the useful signal or only interfering noise signals are present. 
   The invention presented here essentially differs from all systems for the suppression of noise published up until now, in particular by the special stochastic gradient process, the transformation of the signals for the updating of the filter coefficients as well as by the interaction of compensation filters and standardization unit in the controlling of the adaptation speed. 
   Overall, the system in accordance with the invention within a very great range of signal to noise ratios manifests a consistent characteristic, i.e., the signal to noise ratio is always improved and never degraded. It is therefore in a position to make an optimum contribution to better hearing in difficult acoustic situations. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the following, the invention is described in detail on the basis of Figures. 
     These in the form of block diagrams illustrate: 
       FIG. 1  a general system for the adaptive suppression of noise by means of the method of the blind signal separation in accordance with the state of prior art, 
       FIG. 2  the system in accordance with the invention, 
       FIG. 3  a detailed drawing of a compensation filter of the system in accordance with the invention, 
       FIG. 4  a detailed drawing of a retarding element of the system in accordance with the invention, 
       FIG. 5  a detailed drawing of a filter of the system in accordance with the invention, 
       FIG. 6  a detailed drawing of a cross-over element filter of the system in accordance with the invention, 
       FIG. 7  a detailed drawing of a cross-correlator of the system in accordance with the invention, 
       FIG. 8  a detailed drawing of a pre-calculation unit of the type V of the system in accordance with the invention, 
       FIG. 9  a detailed drawing of a pre-calculation unit of the type B of the system in accordance with the invention, 
       FIG. 10  a detailed drawing of an updating unit of the system in accordance with the invention, 
       FIG. 11  a detailed drawing of a cross-over element de-correlator of the system in accordance with the invention, 
       FIG. 12  a detailed drawing of a smoothing unit of the system in accordance with the invention, and 
       FIG. 13  a detailed drawing of a standardization unit of the system in accordance with the invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
   A general system for the adaptive noise suppression by means of the method of the blind signal separation, as it is known from prior art, is illustrated in FIG.  1 . Two microphones  1  and  2  provide the electric signals d 1 (t) and d 2 (t). The following AD—converters  3  and  4  from these calculate digital signals at the discrete points in time d 1 (n·T) and d 2 (n.T), in abbreviated notation d 1 (n) and d 2 (n) or d 1  and d 2 . In this, T=1/f s  is the scanning period, f s  the scanning frequency and n a consecutive index. Following then are the compensation filters  5  and  6  that, depending on the application, can carry out a fixed frequency response correction on the individual microphone signals. The input signals y 1  and y 2  resulting from this are now in accordance with  FIG. 1  brought both to retarding elements  7  and  8  as well as to filters  17  and  18 . Subtractors  9  and  10  following supply output signals s 1  and s 2 . 
   Following afterwards are processing units  11  and  12  that, depending on the application, carry out any linear or non-linear post-processing required. Their output signals u 1  and u 2  through DA—converters  13  and  14  can be converted into electric signals u 1 (t) and u 2 (t) and made audible by means of loudspeakers, resp., earphones  15  and  16 . 
   It is the objective of the blind signal separation, starting out from the input signals y 1  and y 2  and by means of the filters Filter  17  and  18 , to obtain output signals s 1  and s 2 , which are statistically independent to as great an extent as possible. For those acoustic signals, which are stationary respectively only for a short time period, the requirement of uncorrelated output signals s 1  and s 2  is sufficient. For the calculation of the optimum filter coefficients  w   1  and  w   2  in the filters  17  and  18 , we shall minimize a cost function. This is the following quadratic cost function J consisting of cross-correlation terms. In it, the operator * stands for conjugate-complex in applications, where we are dealing with complex-value signals. 
       J   =         ∑     l   =     -     L   l           L   u       ⁢           ⁢              R       s   1     ⁢     s   2         ⁡     (   l   )            2       =       ∑     l   =     -     L   l           L   u       ⁢         R       s   1     ⁢     s   2         ⁡     (   l   )       ·       R         s   1     ⁢     s   2       ⁢             *     ⁡     (   l   )                 
 
   The cross-correlation terms can be expressed with the help of the output signals s 1  and s 2 . In doing so, the operator E[] stands for the expectancy value.
 
 R   s     1     s     2   ( l )= E[s   1 *( n )·s 2 ( n+l )]
 
   The output signals s 1  and s 2  can be expressed by the input signals y 1  and y 2  and by means of the filter coefficients  w   1  and  w   2 . In doing so, w 1k  designates the elements of the vector  w   1  and w 2k  the elements of the vector  w   2 . 
                 s   1     ⁡     (   n   )       =         y   1     ⁡     (     n   -     D   1       )       -       ∑     k   =   0       N   1       ⁢           ⁢         w     1   ⁢   k     *     ⁡     (   n   )       ·       y   2     ⁡     (     n   -   k     )                             s   2     ⁡     (   n   )       =         y   2     ⁡     (     n   -     D   2       )       -       ∑     k   =   0       N   2       ⁢           ⁢         w     2   ⁢   k     *     ⁡     (   n   )       ·       y   1     ⁡     (     n   -   k     )                       
 
   For the minimization of the cost function J by means of a gradient process, the derivations with respect to the filter coefficients  w   1  and  w   2  have to be calculated. After a few transformations, we obtain the following expressions. 
                 ∂   J       ∂       w     1   ⁢   k       ⁡     (   n   )           =       -   2     ⁢       ·   ∑       l   =     -     L   l           L   u       ⁢         R       y   2     ⁢     s   2       *     ⁡     (     k   +   l     )       ·     R       s   1     ⁢     s   2           ⁢           ⁢     (   l   )                       ∂   J       ∂       w     2   ⁢   k       ⁡     (   n   )           =       -   2     ⁢       ·   ∑       l   =     -     L   l           L   u       ⁢         R       y   1     ⁢     s   1       *     ⁡     (     k   -   l     )       ·       R       s   1     ⁢     s   2       *     ⁡     (   l   )                     
 
   For the deduction of the stochastic gradient process in accordance with the invention, now the summation limits have to be replaced by limits dependent on the coefficient index. To carry this out, the following substitutions are necessary.
 
 L   1   =L   2   −D   2   +k L   u   =L   2   +D   2   −k 
 
 L   1   =L   1   +D   1   −k L   u   =L   1   −D   1   =k 
 
   The derivations can now be expressed with the modified summation limits. 
                 ∂   J       ∂       w     1   ⁢   k       ⁡     (   n   )           =       -   2     ·       ∑     l   =     -     (       L   2     -     D   2       )             L   2     +     D   2         ⁢           R       y   2     ⁢     s   2       *     ⁡     (   l   )       ·     R       s   1     ⁢     s   2           ⁢           ⁢     (     l   -   k     )                           ∂   J       ∂       w     2   ⁢   k       ⁡     (   n   )           =       -   2     ·       ∑     l   =     -     (       L   1     -     D   1       )             L   1     +     D   1         ⁢           R       y   1     ⁢     s   1       *     ⁡     (   l   )       ·     R       s   1     ⁢     s   2           ⁢           ⁢     (     k   -   l     )                     
 
   During the transition from the normal gradient to the stochastic gradient, expectancy values are substituted by momentary values. In the case of the method in accordance with the invention, this is carried out for the cross-correlation terms of the output signals s 1  and s 2 . In doing so, the latest available momentary values are made use of in accordance with the following relationship. 
           R       s   1     ⁢     s   2         ⁡     (   l   )       =       E   ⁡     [         s   1   *     ⁡     (   n   )       ·       s   2     ⁡     (     n   +   l     )         ]       ≈     {                 s   1   *     ⁡     (   n   )       ·       s   2     ⁡     (     n   +   l     )                       s   1   *     ⁡     (     n   -   l     )       ·       s   2     ⁡     (   n   )               ⁢           (     l   &lt;   0     )               (     l   ≥   0     )                     
 
   By the insertion of the momentary values, the calculation of the derivations is simplified and we obtain the following relationships. The intermediate values v 1 , b 1 , v 2  and b 2  make possible a simplified notation and also a simplified calculation, because at any discrete point in time of every value respectively only one new value has to be calculated. As a result of this novel procedure, in the method according to the present invention the calculation effort is significantly reduced. 
                       v   1     ⁡     (   n   )       =       ∑     l   =   0         L   2     +     D   2         ⁢         R       y   2     ⁢     s   2       *     ⁡     (   l   )       ·       s   1   *     ⁡     (     n   -   l     )                           b   1     ⁡     (   n   )       =       ∑     l   =     -     (       L   2     -     D   2       )           -   1       ⁢         R       y   2     ⁢     s   2       *     ⁡     (   l   )       ·       s   2     ⁡     (     n   +   l     )                           v   2     ⁡     (   n   )       =       ∑     l   =   0         L   1     +     D   1         ⁢         R       y   1     ⁢     s   1       *     ⁡     (   l   )       ·       s   2   *     ⁡     (     n   -   l     )                           b   2     ⁡     (   n   )       =       ∑     l   =     -     (       L   1     -     D   1       )           -   1       ⁢         R       y   1     ⁢     s   1       *     ⁡     (   l   )       ·       s   1     ⁡     (     n   +   l     )                           ∂   J       ∂       w     1   ⁢   k       ⁡     (   n   )           =       -   2     ·     [           v   1     ⁡     (   n   )       ·       s   2     ⁡     (     n   -   k     )         +         b   1     ⁡     (     n   -   k     )       ·       s   1   *     ⁡     (   n   )           ]                       ∂   J       ∂       w     2   ⁢   k       ⁡     (   n   )           =       -   2     ·     [           v   2     ⁡     (   n   )       ·       s   1     ⁡     (     n   -   k     )         +         b   2     ⁡     (     n   -   k     )       ·       s   2   *     ⁡     (   n   )           ]                                   
 
   The updating of the filter coefficients  w   1  and  w   2  now takes place in the direction of the negative gradient. In doing this, μ is the width of the step. One obtains a relationship similar to the familiar LMS—algorithm (Least Mean Square). The two terms per coefficient are solely necessary, because for the momentary value we have utilized the respectively latest estimated values. This makes sense, if we want to achieve a rapidly reacting behaviour characteristic.
 
 w   1k ( n +1)= w   1k ( n )+μ·[ v   1 ( n )· s   2 ( n−k )+ b   1 ( n−k )· s   1 *( n )]
 
 w   2k ( n +1)= w   2k ( n )+μ·[ v   2 ( n )· s   1 ( n−k )+ b   2 ( n−k )· s   2 *( n )]
 
   In order to obtain a uniform behaviour characteristic, we formulate a standardized version for the updating of the filter coefficients  w   1  and  w   2 . The standardization value has to be proportional to the square of a power value p 1 , resp., p 2 . In this, β is the adaptation speed. 
           w     1   ⁢   k       ⁡     (     n   +   1     )       =         w     1   ⁢   k       ⁡     (   n   )       +       β       [       p   1     ⁡     (   n   )       ]     2       ·     [           v   1     ⁡     (   n   )       ·       s   2     ⁡     (     n   -   k     )         +         b   1     ⁡     (     n   -   k     )       ·       s   1   *     ⁡     (   n   )           ]             
           w     2   ⁢   k       ⁡     (     n   +   1     )       =         w     2   ⁢   k       ⁡     (   n   )       +       β       [       p   2     ⁡     (   n   )       ]     2       ·     [           v   2     ⁡     (   n   )       ·       s   1     ⁡     (     n   -   k     )         +         b   2     ⁡     (     n   -   k     )       ·       s   2   *     ⁡     (   n   )           ]             
 
   The system described up to now for the adaptive suppression of noise by means of the method of the blind signal separation, because of the not to be neglected auto-correlation function of real acoustic signals, is not yet sufficient to achieve a processing with low distortion and with a simultaneously satisfactory convergence characteristic in a realistic environment. The system can be improved, if updating of the filter coefficients  w   1  and  w   2  is not directly based on the input signals y 1  and y 2  and the output signals s 1  and s 2 , but rather on transformed signals. 
   The system in accordance with the invention according to  FIG. 2  utilizes four cross-over element filters  19 ,  20 ,  21  and  22  for the signal-dependent transformation of the input and output signals. For the rapid signal-dependent transformation, the cross-over element filter structures known from speech signal processing prove to be particularly suitable. There they are utilized for the linear prediction. 
   For the determination of the coefficients  k  of the cross-over element filters, two cross-over element de-correlators  31  and  32  and a smoothing unit  33  are present. The cross-over element de-correlators each respectively determine a coefficient vector  k   1  and  k   2  based on the input signals y 1  and y 2 . In the smoothing unit, the mean of the two coefficient vectors is taken and smoothed over time is passed on to the cross-over element filters as coefficient vector  k . 
   In contrast to the known system from  FIG. 1 , in the system in accordance with the invention all calculations for the updating of the coefficients are based on the transformed input—and output signals y 1M , y 2M , s 1M  and s 2M . Two cross-correlators  23  and  24  calculate the necessary cross-correlation vectors  r   1  and  r   2 . The pre-calculation units  25 ,  26 ,  27  and  28  determine the intermediate values v 1 , v 2 , b 1  and b 2 . The updating units  29  and  30  determine the modified filter coefficients  w   1  and  w   2  and make them available to the filters  17  and  18 . 
   In the standardization unit  34 , a common standardization value p is calculated for the updating of the filter coefficients  w   1  and  w   2 . The optimum selection of the standardization value p together with the correct adjustment of the compensation filters  5  and  6  assure a clean and unequivocal convergence characteristic of the method in accordance with the invention. 
   In the following, a special embodiment of the invention presented here is described in more detail starting out from FIG.  2 . The microphones  1  and  2 , the AD—converters  3  and  4 , the DA—converters  13  and  14  as well as the earphones  15  and  16  are assumed to be ideal in the consideration. The characteristics of the real acoustic—and electric converters can be taken into consideration in the compensation filters  5  and  6 , resp., in the processing units  11  and  12  and, if so required, compensated. For the AD—converters  3  and  4  and the DA—converters  13  and  14 , the following relationships are applicable. In these, T and f s  designate the scanning period, resp., the scanning frequency and the index n the discrete point in time.
 
 d   1 ( n·T )=&gt; d   1 ( n ) u   1 ( n )=&gt; u   1 ( n·T )
 
 d   2 ( n·T )=&gt; d   2 ( n ) u   2 ( n )=&gt; u   2 ( n·T )
 
 T =1/ f   s   f   s =16 kHz
 
   The compensation filter  5  and  6  are designed in accordance with FIG.  3  and the following relationships are applicable. The structure corresponds to a general recursive filter of the order K. The coefficients b 1k , a 1k , b 2k  and a 2k  are set in such a manner, that the mean frequency response on one input equalizes to the other input. In doing so, in preference a mean is taken over all possible locations of acoustic signal sources, resp., over all possible directions of impingement. 
           y   1     ⁡     (   n   )       =       1     a   10       ·     [         ∑     k   =   0     K     ⁢           ⁢       b     1   ⁢   k       ·       d   1     ⁡     (     n   -   k     )           -       ∑     k   =   1     K     ⁢           ⁢       a     1   ⁢   k       ·       y   1     ⁡     (     n   -   k     )             ]           
           y   2     ⁡     (   n   )       =       1     a   20       ·     [         ∑     k   =   0     K     ⁢           ⁢       b     2   ⁢   k       ·       d   2     ⁡     (     n   -   k     )           -       ∑     k   =   1     K     ⁢           ⁢       a     2   ⁢   k       ·       y   2     ⁡     (     n   -   k     )             ]           
       K   =   2       
 
   The retarding elements  7  and  8  are designed in accordance with FIG.  4  and the following relationships are applicable. The necessary retarding times D 1  and D 2  are primarily dependent on the distance of the two microphones and on the preferred sound impingement direction. Small retarding times are desirable, because with this also the overall delay time of the system is reduced.
 
 z   1 ( n )= y   1 ( n−D   1 )
 
 z   2 ( n )= y   2 ( n−D   2 )
 
 D   1   =D   2 =1
 
   For the subtractors  9  and  10 , the following relationships are applicable.
 
 s   1 ( n )= z   1 ( n )− e   1 ( n )
 
 s   2 ( n )= z   2 ( n )− e   2 ( n )
 
   For the processing units  11  and  12 , the following relationships are applicable. The functions f 1 ( ) and f 2 ( ) stand for any linear or non-linear functions and their arguments. They result on the basis of the conventional processing specific to hearing aids.
 
 u   1 ( n )= f   1 ( s   1 ( n ), s   1 ( n −1), s   1 ( n −2), . . . )
 
 u   2 ( n )= f   2 ( s   2 ( n ), s   2 ( n −1), s   2 ( n −2), . . . )
 
   The filters  17  and  18  are designed in accordance with FIG.  5  and the following relationships are applicable. The filter orders N 1  and N 2  are the result of a compromise between achievable effect and the calculation effort. 
           e   1     ⁡     (   n   )       =       ∑     k   =   0       N   1       ⁢         w     1   ⁢   k       ⁡     (   n   )       ·       y   2     ⁡     (     n   -   k     )               
           e   2     ⁡     (   n   )       =       ∑     k   =   0       N   2       ⁢         w     2   ⁢   k       ⁡     (   n   )       ·       y   1     ⁡     (     n   -   k     )               
         N   1     =       N   2     =   63         
 
   The cross-over element filters  19 ,  20 ,  21  and  22  are designed in accordance with FIG.  6  and the following relationships are applicable. The filter order M can be selected as quite small. 
                       y   10     ⁡     (   n   )       =       y   1     ⁡     (   n   )         ⁢     
     ⁢         x   10     ⁡     (   n   )       =       y   1     ⁡     (   n   )         ⁢     
     ⁢               y     1   ⁢   i       ⁡     (   n   )       =         y     1   ⁢     (     i   -   1     )         ⁡     (   n   )       +         k   i     ⁡     (   n   )       ·       x     1   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                           x     1   ⁢   i       ⁡     (   n   )       =           k   i     ⁡     (   n   )       ·       y     1   ⁢     (     i   -   1     )         ⁡     (   n   )         +       x     1   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                   }     ⁢           ⁢     (     1   ≤   i   ≤   M     )       ⁢     
     ⁢         y   20     ⁡     (   n   )       =           y   2     ⁡     (   n   )       ⁢     
     ⁢       x   20     ⁡     (   n   )         =         y   2     ⁡     (   n   )       ⁢     
     ⁢               y     2   ⁢   i       ⁡     (   n   )       =         y     2   ⁢     (     i   -   1     )         ⁡     (   n   )       +         k   i     ⁡     (   n   )       ·       x     2   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                           x     2   ⁢   i       ⁡     (   n   )       =           k   i     ⁡     (   n   )       ·       y     2   ⁢     (     i   -   1     )         ⁡     (   n   )         +       x     2   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                         }     ⁢           ⁢                 ⁢       (     1   ≤   i   ≤   M     )     ⁢     
     ⁢         s   10     ⁡     (   n   )       =           s   1     ⁡     (   n   )       ⁢     
     ⁢       x   30     ⁡     (   n   )         =         s   1     ⁡     (   n   )       ⁢     
     ⁢               s     1   ⁢   i       ⁡     (   n   )       =         s     1   ⁢     (     i   -   1     )         ⁡     (   n   )       +         k   i     ⁡     (   n   )       ·       x     3   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                           x     3   ⁢   i       ⁡     (   n   )       =           k   i     ⁡     (   n   )       ·       s     1   ⁢     (     i   -   1     )         ⁡     (   n   )         +       x     3   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                         }     ⁢           ⁢                 ⁢         (     1   ≤   i   ≤   M     )     ⁢     
     ⁢       s   20     ⁡     (   n   )         =           s   2     ⁡     (   n   )       ⁢     
     ⁢       x   40     ⁡     (   n   )         =         s   2     ⁡     (   n   )       ⁢     
     ⁢               s     2   ⁢   i       ⁡     (   n   )       =         s     2   ⁢     (     i   -   1     )         ⁡     (   n   )       +         k   i     ⁡     (   n   )       ·       x     4   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                           x     4   ⁢   i       ⁡     (   n   )       =           k   i     ⁡     (   n   )       ·       s     2   ⁢     (     i   -   1     )         ⁡     (   n   )         +       x     4   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                       }     ⁢           ⁢     (     1   ≤   i   ≤   M     )         
       M   =   2       
 
   The cross-correlators  23  and  24  are designed in accordance with FIG.  7  and the following relationships are applicable. The constants g and h, which determine the time characteristic of the averaged cross-correlators, should be adapted to the filter orders N 1  and N 2 . The constants L 1  and L 2  determine, how many cross-correlation terms are respectively taken into consideration in the following calculations. 
           r     1   ⁢   k       ⁡     (   n   )       =     {                 g   ·       r     1   ⁢   k       ⁡     (     n   -   1     )         +       h   ·       y     1   ⁢   M       ⁡     (   n   )       ⁢           ·       s     1   ⁢   M       ⁡     (     n   +   k     )         ⁢           ⁢     (       -     (       L   1     -     D   1       )       ≤   k   ≤     -   1       )                       g   ·       r     1   ⁢   k       ⁡     (     n   -   1     )         +       h   ·     y     1   ⁢   M         ⁢       (     n   -   k     )     ·       s     1   ⁢   M       ⁡     (   n   )         ⁢           ⁢     (     0   ≤   k   ≤     (       L   1     +     D   1       )       )         ⁢                   ⁢     
     ⁢       r     2   ⁢   k       ⁡     (   n   )         =     {                 g   ·       r     2   ⁢   k       ⁡     (     n   -   1     )         +       h   ·       y     2   ⁢   M       ⁡     (   n   )       ⁢           ·       s     2   ⁢   M       ⁡     (     n   +   k     )         ⁢           ⁢     (       -     (       L   2     -     D   2       )       ≤   k   ≤     -   1       )                       g   ·       r     2   ⁢   k       ⁡     (     n   -   1     )         +       h   ·     y     2   ⁢   M         ⁢       (     n   -   k     )     ·       s     2   ⁢   M       ⁡     (   n   )         ⁢           ⁢     (     0   ≤   k   ≤     (       L   2     +     D   2       )       )         ⁢                   ⁢     
     ⁢   g     =         63   /   64     ⁢           ⁢   h     =       1   -   g     =         1   /   64     ⁢     
     ⁢     L   1       =       L   2     =   31                       
 
   The pre-calculation units of the type V  25  and  26  are designed in accordance with FIG.  8  and the following relationships are applicable. The standardization has been selected in such a manner, that the intermediate values v 1  and v 2  are dimensionless. 
           v   1     ⁡     (   n   )       =       1       [     p   ⁡     (   n   )       ]       3   2         ·     [       ∑     k   =   0         L   2     +     D   2         ⁢         r     2   ⁢   k       ⁡     (   n   )       ·       s     1   ⁢   M       ⁡     (     n   -   k     )           ]           
           v   2     ⁡     (   n   )       =       1       [     p   ⁡     (   n   )       ]       3   2         ·     [       ∑     k   =   0         L   1     +     D   1         ⁢         r     1   ⁢   k       ⁡     (   n   )       ·       s     2   ⁢   M       ⁡     (     n   -   k     )           ]           
 
   The pre-calculation units of the type B  27  and  28  are designed in accordance with FIG.  9  and the following relationships are applicable. The standardization has been selected in such a manner, that the intermediate values b 1  and b 2  are dimensionless. 
           b   1     ⁡     (   n   )       =       1       [     p   ⁡     (   n   )       ]       3   2         ·     [       ∑     k   =     -     (       L   2     -     D   2       )           -   1       ⁢         r     2   ⁢   k       ⁡     (   n   )       ·       s     2   ⁢   M       ⁡     (     n   +   k     )           ]           
           b   2     ⁡     (   n   )       =       1       [     p   ⁡     (   n   )       ]       3   2         ·     [       ∑     k   =     -     (       L   1     -     D   1       )           -   1       ⁢         r     1   ⁢   k       ⁡     (   n   )       ·       s     1   ⁢   M       ⁡     (     n   +   k     )           ]           
 
   The updating units  29  and  30  are designed in accordance with FIG.  10  and the following relationships are applicable. The adaptation speed β can be selected in correspondence with the desired convergence characteristic. 
           w     1   ⁢   k       ⁡     (     n   +   1     )       =         w     1   ⁢   k       ⁡     (   n   )       +         β       p   ⁡     (   n   )           ·     [           v   1     ⁡     (   n   )       ·       s     2   ⁢   M       ⁡     (     n   -   k     )         +         b   1     ⁡     (     n   -   k     )       ·       s     1   ⁢   M       ⁡     (   n   )           ]       ⁢           ⁢     (     0   ≤   k   ≤     N   1       )             
           w     2   ⁢   k       ⁡     (     n   +   1     )       =         w     2   ⁢   k       ⁡     (   n   )       +         β       p   ⁡     (   n   )           ·     [           v   2     ⁡     (   n   )       ·       s     1   ⁢   M       ⁡     (     n   -   k     )         +         b   2     ⁡     (     n   -   k     )       ·       s     2   ⁢   M       ⁡     (   n   )           ]       ⁢           ⁢     (     0   ≤   k   ≤     N   2       )             
 
   The cross-over element de-correlators  31  and  32  are designed in accordance with FIG.  11  and the following relationships are applicable. The cross-over element de-correlators calculate the coefficient vectors  k   1  and  k   2 , which are required for a de-correlation of their input signals. 
                       f   10     ⁡     (   n   )       =       y   1     ⁡     (   n   )         ⁢     
     ⁢         b   10     ⁡     (   n   )       =       y   1     ⁡     (   n   )         ⁢     
     ⁢               f     1   ⁢   i       ⁡     (   n   )       =         f     1   ⁢     (     i   -   1     )         ⁡     (   n   )       +         k     1   ⁢   i       ⁡     (     n   -   1     )       ·       b     1   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                           b     1   ⁢   i       ⁡     (   n   )       =           k     1   ⁢   i       ⁡     (     n   -   1     )       ·       f     1   ⁢     (     i   -   1     )         ⁡     (   n   )         +       b     1   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                         d     1   ⁢   i       ⁡     (   n   )       =       g   ·       d     1   ⁢   i       ⁡     (     n   -   1     )         +     h   ·     [         (       f     1   ⁢     (     i   -   1     )         ⁡     (   n   )       )     2     +       (       b     1   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )       )     2       ]                         n     1   ⁢   i       ⁡     (   n   )       =       g   ·       n     1   ⁢   i       ⁡     (     n   -   1     )         +     h   ·     [       (     -   2     )     ·       f     1   ⁢     (     i   -   1     )         ⁡     (   n   )       ·       b     1   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )         ]                         k     1   ⁢   i       ⁡     (   n   )       =         n     1   ⁢   i       ⁡     (   n   )           d     1   ⁢   i       ⁡     (   n   )                   }     ⁢                 ⁢           ⁢               (     1   ≤           ⁢   i   ≤           ⁢   M     )     ⁢     
     ⁢       f   20     ⁡     (   n   )         =           y   2     ⁡     (   n   )       ⁢     
     ⁢       b   20     ⁡     (   n   )         =         y   2     ⁡     (   n   )       ⁢     
     ⁢               f     2   ⁢   i       ⁡     (   n   )       =         f     2   ⁢     (     i   -   1     )         ⁡     (   n   )       +         k     2   ⁢   i       ⁡     (     n   -   1     )       ·       b     2   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                           b     2   ⁢   i       ⁡     (   n   )       =           k     2   ⁢   i       ⁡     (     n   -   1     )       ·       f     2   ⁢     (     i   -   1     )         ⁡     (   n   )         +       b     2   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )                         d     2   ⁢   i       ⁡     (   n   )       =       g   ·       d     2   ⁢   i       ⁡     (     n   -   1     )         +     h   ·     [         (       f     2   ⁢     (     i   -   1     )         ⁡     (   n   )       )     2     +       (       b     2   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )       )     2       ]                         n     2   ⁢   i       ⁡     (   n   )       =       g   ·       n     2   ⁢   i       ⁡     (     n   -   1     )         +     h   ·     [       (     -   2     )     ·       f     2   ⁢     (     i   -   1     )         ⁡     (   n   )       ·       b     2   ⁢     (     i   -   1     )         ⁡     (     n   -   1     )         ]                         k     2   ⁢   i       ⁡     (   n   )       =         n     2   ⁢   i       ⁡     (   n   )           d     2   ⁢   i       ⁡     (   n   )                       }       ⁢                 ⁢           ⁢           (           ⁢     1   ⁢           ≤           ⁢   i   ⁢           ≤           ⁢   M     ⁢           )           
 
   The smoothing unit  33  is designed in accordance with FIG.  12  and the following relationships are applicable. The constants f and l are selected in such a manner, that the averaged coefficients  k  obtain the required smoothed course. 
                     d   i     ⁡     (   n   )       =     f   ·     [             k     1   ⁢   i       ⁡     (   n   )       +       k     2   ⁢   i       ⁡     (   n   )         2     -       k   i     ⁡     (     n   -   1     )         ]                       k   i     ⁡     (   n   )       =         k   i     ⁡     (     n   -   1     )       +         d   i     ⁡     (   n   )       ·     min   ⁡     (         (       d   i     ⁡     (   n   )       )     2     ,   l     )                   }     ⁢           ⁢     (     1   ≤   i   ≤   M     )         
       f   =       1.0   ⁢           ⁢   l     =   0.25         
 
   The standardization unit  34  is designed in accordance with FIG.  13  and the following relationships are applicable. First the four powers of y 1M , y 2M , s 1M  and s 2M  are calculated and from this the standardization value p is determined. 
           i   1     ⁡     (   n   )       =       g   ·       i   1     ⁡     (     n   -   1     )         +     h   ·       [       y     1   ⁢   M       ⁡     (   n   )       ]     2             
           o   1     ⁡     (   n   )       =       g   ·       o   1     ⁡     (     n   -   1     )         +     h   ·       [       s     1   ⁢   M       ⁡     (   n   )       ]     2             
           i   2     ⁡     (   n   )       =       g   ·       i   2     ⁡     (     n   -   1     )         +     h   ·       [       y     2   ⁢   M       ⁡     (   n   )       ]     2             
           o   2     ⁡     (   n   )       =       g   ·       o   2     ⁡     (     n   -   1     )         +     h   ·       [       s     2   ⁢   M       ⁡     (   n   )       ]     2             
         p   ⁡     (   n   )       =     max   ⁡     (             i   1     ⁡     (   n   )       +       o   1     ⁡     (   n   )         2     ,           i   2     ⁡     (   n   )       +       o   2     ⁡     (   n   )         2       )           
 
   The preferred embodiment without any problem can be programmed on a commercially available signal processor or implemented in an integrated circuit. To do this, all variables have to be suitably quantified and the operations optimized with a view to the architecture blocks present. In doing so, particular attention has to be paid to the treatment of the quadratic values (powers) and the division operations. Dependent on the target system, there are optimized procedures for this in existence. These, however, as such are not object of the invention presented here.