Abstract:
In a method and an acoustic system that generate a stereo signal for each of multiple. separate sources, a blind source separation of at least two microphone signals is conducted to acquire BSS filters. Each of the microphone signals is filtered with its own filter transfer function that is the quotient of a power density spectral portion of the respective sound source and the overall power density spectrum of the respective microphone signal, such that two stereo signals are obtained for each microphone signal. An approximation of the signals to be separated, for example for each of two hearing devices, is thereby possible.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention concerns a method for respectively generating stereo signals for at least two sound sources. Moreover, the present invention concerns a corresponding acoustic system for generation of stereo signals. The present invention in particular concerns hearing devices such as hearing aid devices. 
     2. Description of the Prior Art 
     A method for generating respective mono (monaural) signals for each of multiple sound sources is known from the essay by J. Benesty, Y. Huang: Adaptive Signal Processing: Berlin, N.Y., pages 195-23, 2003. The BSS methods (blind source separation) described therein can separate and individually reproduce spatially-separate but temporally-overlapping sources. Such a BSS method can be used, for example, as a binaural feed or especially for a binaural directional microphone, whereby a microphone signal from the right hearing device is used as well as a microphone signal from the left hearing device. 
     A problem that still has yet to be solved is that the BSS method provides only a mono signal for each of the separate sources. If the hearing device user were to be identically provided with this signal at both hearing devices, the user could in fact perceive the sources with very good separation, but spatial localization of the sources would not be possible. For this purpose, the right and left signals would have to be differentiated at the inter-aural level and delay differences that are typical for natural signals would have to be introduced. 
     Alternative methods to the BSS methods for binaural directional microphony exhibit a very limited capability and for this reason (as well as due to the usually absent wireless connection between hearing devices) are not used. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to provide a method and acoustic sound system for better perception capability of separate sound sources. 
     This object is inventively achieved by a method for generation of respective stereo signals for at least two separate sound sources by conducting a blind source separation of at least two microphone signals to acquire transfer functions of filters of a first filter device, determining transfer functions of filters of a second filter device, using the transfer functions of the filters of the first filter device (the transfer functions of the filters of the second filter device respectively corresponding to the quotients of a power density spectral fraction of the respective sound sources and the overall power density spectrum of the respective microphone signals, and filtering the at least two microphone signals, respectively with at least two filters of the second filter device, such that two stereo signals are obtained for each microphone signal. 
     The above object also is inventively achieved by a method for generation of stereo signals for at least two separate sound sources by conducting a blind source separation of at least two microphone signals using a first filter device for acquisition of two mono output signals, and respectively filtering the mono output signals with at least two second filters of a second filter device, the transfer functions of which are calculated from the transfer functions of the filters of the first filter device, such that two stereo signals are attained for each mono output signal. The transfer functions from the sound sources to the microphones can be calculated and multiplied with the mono output signals, so the transfer functions of the second filters can be obtained. 
     The above object also is inventively achieved by an acoustic system for generation of respective stereo signals for at least two separate sound sources, having a microphone device that provides at least two microphone signals, a first filter device for blind source separation of the at least two microphone signals based on transfer functions of filters of the first filter device, a second filter device for filtering of each of the microphone signals such that two stereo signals are generated for each microphone signal, and a calculation device computer to determine the transfer functions of filters of the second filter device using the transfer functions of the filters of the first filter device, the transfer functions of the filter of the second filter device respectively corresponding to the quotients of a power density spectral portion of the respective sound sources and the overall power density spectrum of the respective microphone signals. 
     The above object also is inventively achieved by an acoustic system for generation of respective stereo signals for at least two separate sound sources, having a microphone device that provides at least two microphone signals, a first filter device for blind source separation of the at least two microphone signals based on the transfer functions of filters of the first filter device to produce two mono output signals, a second filter device for filtering of each of the microphone signals such that two stereo signals are generated from each mono output signal, and a calculation device to determine the transfer functions of filters of the second filter device using the transfer functions of the filters of the first filter device. 
     The approximation of the signals to be separated, for example for each hearing device, headset or the like, is possible by means of inventive method and the inventive acoustic system. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram representing a signal model and a BSS method according to the prior art. 
         FIG. 2  is a block diagram showing a first embodiment of an inventive acoustic system to provide a binaural output (stereo output). 
         FIG. 3  is a block diagram of a second embodiment of an inventive acoustic system to provide a binaural output (stereo output). 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The exemplary embodiments subsequently illustrated in detail represent preferred embodiments of the present invention. 
     A BSS method is used to realize a binaural directional microphone with stereo or, respectively, binaural reproduction. BSS methods can generally be explained using  FIG. 1 . Reference is made again in this regard to the essay by J. Benesty and Y. Huang. The signal transfer from two signal sources to two microphones is correspondingly described via the signal model SIG. The further processing from the microphones to the output is shown by a BSS model BSS. 
     The signals s 1 ( k ) of the first signal source and the signals s 2 ( k ) of the second signal source are correspondingly transferred to both microphones, whereby k represents sample points in time. The transfer functions in the spectral range for the individual transfer paths can be symbolized by signal model filters H ij (Ω). At the microphones, the signals of both signal sources can be additively superimposed on the microphone signals x 1 ( k ) and x 2 ( k ). 
     The BSS model corresponding to  FIG. 1  is now applied in order to now again separate the individual signal portions. A mono output signal y 1 ( k ) and y 2 ( k ) is thereby respectively determined for each source from the microphone signals x 1 ( k ) and y 2 ( k ) with the aid of adaptive BSS filters W ij (Ω). 
     The following correlation between the signal model filters H ij (Ω) and the adaptive BSS filters W ij (Ω) applies for BSS: 
     
       
         
           
               
             
               
                 
                   
                     
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     BSS methods now determine the filter values W 11 (Ω), W 12 (Ω), W 21 (Ω) and W 22 (Ω). The signal model filters H 11 (Ω), H 12 (Ω), H 21 (Ω) and H 22 (Ω) and the complex weightings c 1 (Ω) and c 2 (Ω) of the signals after separation. The matrix equation above can now be solved for H 11 (Ω), H 12 (Ω), H 21 (Ω) and H 22 (Ω). The result of this is: 
     
       
         
           
             
               
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     It is the goal to obtain stereo signals that are transferred to the right and left hearing devices and allow a spatial perception by the hearing device user. 
     Two method versions are now introduced in the following with which it is possible to calculate the desired binaural signals for both separate sources. 
     1) Calculation of the Stereo or, Respectively, Binaural Signals with the Aid of Wiener Filters 
     Corresponding to the first method according to  FIG. 2 , the Wiener filters are calculated for the BSS method. The output signals y 1 ( k ) and y 2 ( k ) of the BSS method are no long necessary for the further processing. However, the filters W ij (Ω) of the BSS with i=1, 2 and j=1, 2 are used. Post-processing filters G ij (Ω) with i=1, 2 and j=1, 2 are calculated from the filter values W ij (Ω) as this is indicated in  FIG. 2  by the arrow from the filter BSS to the filter G. 
     Via the filter G, the left microphone signal x 1 ( k ) and the right microphone signal x 2 ( k ) are now filtered such that the stereo output signals z 1 left(k), z 1 right(k), z 2 left(k) and z 2 right(k) for the binaural feed or stereo feed result. For this the left microphone signal x 1 ( k ) is filtered by the filter units G 11 (Ω) and G 12 (Ω). The right microphone signal x 2 ( k ) is accordingly filtered by the filter units G 21 (Ω) and G 22 (Ω) in order to obtain the stereo signals of the individual sound sources for the right channel. 
     If the above equations are used, the power density spectra S x1x1 (Ω) and S x2x2 (Ω) of both microphone signals x 1 ( k ) and x 2 ( k ) can be written as follows:
 
 S   x1x1 (Ω)=| {tilde over (H)}   11 (Ω)| 2   |c   1 (Ω)| 2   S   s1s1 (Ω)+| {tilde over (H)}   12 (Ω)| 2   |c   2 (Ω)| 2   S   s2s2 (Ω)
 
 S   x2x2 (Ω)=| {tilde over (H)}   21 (Ω)| 2   |c   1 (Ω)| 2   S   s1s1 (Ω)+| {tilde over (H)}   22 (Ω)| 2   |c   2 (Ω)| 2   S   s2s2 (Ω)
 
     S s1s1 (Ω) and S s2s2 (Ω) thereby mean the power density spectra of both signal sources. 
     If these equations are now solved for the unknown values S s1s1 (Ω)|c 1 (Ω)| 2  and S s2s2 (Ω)|c 2 (Ω)| 2 , the following results: 
     
       
         
           
             
               
                 
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     The portions of the power density spectra of the microphone signals can thus be calculated as follows: 
     1. Power density spectral portion from s 1 ( k ) into x 1 ( k ): 
     
       
         
           
               
             
               
                 
                   
                     
                       
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                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     22 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     2. Power density spectral portion from s 2 ( k ) into x 1 ( k ): 
     
       
         
           
               
             
               
                 
                   
                     
                       
                         P 
                         12 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     = 
                       
                     ⁢ 
                     
                       
                         
                            
                           
                             
                               
                                 H 
                                 ~ 
                               
                               12 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                            
                           
                             
                               c 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                           S 
                           
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             x 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                     ⁢ 
                     
                       
                         
                            
                           
                             
                               
                                 H 
                                 ~ 
                               
                               12 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                           
                             
                               
                                 S 
                                 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 Ω 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                 S 
                                 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 Ω 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     22 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     3. Power density spectral portion from s 1 ( k ) into x 2 ( k ): 
     
       
         
           
               
             
               
                 
                   
                     
                       
                         P 
                         21 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     = 
                       
                     ⁢ 
                     
                       
                         
                            
                           
                             
                               
                                 H 
                                 ~ 
                               
                               21 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                            
                           
                             
                               c 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                           S 
                           
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             ⁢ 
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                     ⁢ 
                     
                       
                         
                            
                           
                             
                               
                                 H 
                                 ~ 
                               
                               21 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                           
                             
                               
                                 S 
                                 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 Ω 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     22 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                 S 
                                 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 Ω 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     22 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     4. Power density spectral portion from s 2 ( k ) into x 2 ( k ): 
     
       
         
           
               
             
               
                 
                   
                     
                       
                         P 
                         22 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     = 
                       
                     ⁢ 
                     
                       
                         
                            
                           
                             
                               
                                 H 
                                 ~ 
                               
                               22 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                            
                           
                             
                               c 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                           S 
                           
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                             ⁢ 
                             s 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                       
                     ⁢ 
                     
                       
                         
                            
                           
                             
                               
                                 H 
                                 ~ 
                               
                               22 
                             
                             ⁡ 
                             
                               ( 
                               Ω 
                               ) 
                             
                           
                            
                         
                         2 
                       
                       ⁢ 
                       
                         
                           
                             
                               
                                 S 
                                 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                   ⁢ 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 Ω 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                 S 
                                 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                   ⁢ 
                                   x 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 Ω 
                                 ) 
                               
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                         
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     22 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                           - 
                           
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   
                                     
                                       H 
                                       ~ 
                                     
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     Ω 
                                     ) 
                                   
                                 
                                  
                               
                               2 
                             
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The four Wiener filters for extraction of the signal portions of S 1 (Ω) and S 2 (Ω) from the microphone signals X 1 (Ω) and X 2 (Ω) thus result into: 
     1. Calculation of the signal portion of S 1 (Ω) in the first microphone: application of the following filter to the signal X 1 (Ω): 
     
       
         
           
             
               
                 G 
                 11 
               
               ⁡ 
               
                 ( 
                 Ω 
                 ) 
               
             
             = 
             
               
                 
                   P 
                   11 
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
               
                 
                   S 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
             
           
         
       
     
     2. Calculation of the signal portion of S 2 (Ω) in the first microphone: application of the following filter to the signal X 1 (Ω): 
     
       
         
           
             
               
                 G 
                 12 
               
               ⁡ 
               
                 ( 
                 Ω 
                 ) 
               
             
             = 
             
               
                 
                   P 
                   12 
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
               
                 
                   S 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
             
           
         
       
     
     3. Calculation of the signal portion of S 1 (Ω) in the second microphone: application of the following filter to the signal X 2 (Ω): 
     
       
         
           
             
               
                 G 
                 21 
               
               ⁡ 
               
                 ( 
                 Ω 
                 ) 
               
             
             = 
             
               
                 
                   P 
                   21 
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
               
                 
                   S 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
             
           
         
       
     
     4. Calculation of the signal portion of S 2 (Ω) in the second microphone: application of the following filter to the signal X 2 (Ω): 
     
       
         
           
             
               
                 G 
                 22 
               
               ⁡ 
               
                 ( 
                 Ω 
                 ) 
               
             
             = 
             
               
                 
                   P 
                   22 
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
               
                 
                   S 
                   
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     x 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                 
                 ⁡ 
                 
                   ( 
                   Ω 
                   ) 
                 
               
             
           
         
       
     
     All necessary values, i.e. the filter values W ij (Ω) from which the values {tilde over (H)} ij (Ω) are calculated as well as the power density spectra S x1x1 (Ω) and S x2x2 (Ω), are available at any point in time or can be instantly approximated. 
     Given this application of the Wiener filtering, the known artifacts as they are known from classical known reduction methods do not occur since all necessary power density spectra can be instantaneously approximated. They do not have to be approximated in a smoothed manner and a discontinuation of the approximation during specific time segments is not necessary. 
     2) Direct Calculation of the Stereo (Binaural) Output Signals Based on the Mono Output Signals of the BSS Method and the Approximated Filter Values W ij (Ω) 
     According to  FIG. 3 , the binaural signal portions or, respectively, stereo signal portions z 1 left(k), z 1 right(k), z 2 left(k) and z 2 right(k) can alternatively also be directly calculated according to the following with the aid of the output signals of the BSS method, y 1 ( k ) and y 2 ( k ), as well as the filter values W ij (Ω) implicitly approximated in the BSS method: 
     1. Calculation of the signal portion of S 1 (Ω) in the first microphone: 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         H 
                         11 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         Y 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                       
                         
                           c 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         c 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         11 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     Y 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         11 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       Y 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                         ( 
                         Ω 
                         ) 
                       
                       ⁢ 
                       
                         
                           W 
                           22 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     
                       
                         
                           
                             W 
                             11 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             22 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           
                             W 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     2. Calculation of the signal portion of S 1 (Ω) in the second microphone: 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         H 
                         21 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         Y 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                         ⁢ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                       
                         
                           c 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         c 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         21 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     Y 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         21 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       Y 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                       ⁢ 
                       
                         ( 
                         Ω 
                         ) 
                       
                       ⁢ 
                       
                         
                           W 
                           21 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     
                       
                         
                           
                             W 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           
                             W 
                             11 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             22 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     3. Calculation of the signal portion of S 2 (Ω) in the first microphone: 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         H 
                         12 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         Y 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                       
                         
                           c 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         c 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         12 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     Y 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         12 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       Y 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         ( 
                         Ω 
                         ) 
                       
                       ⁢ 
                       
                         
                           W 
                           12 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     
                       
                         
                           
                             W 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           
                             W 
                             11 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             22 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     4. Calculation of the signal portion of S 2 (Ω) in the second microphone: 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         H 
                         22 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                   = 
                   
                     
                       
                         Y 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                         ⁢ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                       
                         
                           c 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     ⁢ 
                     
                       
                         c 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         22 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     Y 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                     ⁢ 
                     
                       ( 
                       Ω 
                       ) 
                     
                     ⁢ 
                     
                       
                         
                           H 
                           ~ 
                         
                         22 
                       
                       ⁡ 
                       
                         ( 
                         Ω 
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                   
                     
                       Y 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                       ⁢ 
                       
                         ( 
                         Ω 
                         ) 
                       
                       ⁢ 
                       
                         
                           W 
                           11 
                         
                         ⁡ 
                         
                           ( 
                           Ω 
                           ) 
                         
                       
                     
                     
                       
                         
                           
                             W 
                             11 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             22 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           
                             W 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             W 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             Ω 
                             ) 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     The output signals of the BSS method y 1 ( k ), y 2 ( k ) (Y 1 (Ω) and Y 2 (Ω) in the spectral range) are thus further processed by the filter device {tilde over (H)}. This means that the mono output signal y 1 ( k ) concerning the signal source S 1  is filtered by the filters {tilde over (H)} 11 (Ω) and {tilde over (H)} 21 (Ω) such that the stereo signals z 1 left(k) and z 1 right(k) result for the signal source S 1 . The mono output signal y 2 ( k ) is analogously filtered by both filters {tilde over (H)} 12 (Ω) and {tilde over (H)} 22 (Ω), such that the stereo signals z 2 left(k) and z 2 right(k) result for the signal source S 2 . 
     The filters W ij (Ω) (implicitly approximated in the BSS method) that describe the transfer functions from the sources to the microphones are thus used to calculate the filters H ij (Ω). If these are multiplied with the approximated mono signals Y 1 (Ω) and Y 2 (Ω) corresponding to the equations above, the desired binaural signals are obtained. This calculation is possible since the missing compensation factors c 1  and c 2  for determination of the filter values H ij (Ω) and the source signals S 1 (Ω) and S 2 (Ω) directly cancel in the multiplication. 
     Although modifications and changes may be suggested by those skilled in the art, it is the intention of the inventor to embody within the patent warranted hereon all changes and modifications as reasonably and properly come within the scope of his contribution to the art.