PATENT ABSTRACT
A desired signal is extracted with a higher accuracy from a mixed signal wherein a plurality of signals are mixed. At the time of extracting a first signal from a first mixed signal and a second mixed signal, said first mixed signal and second mixed signal having the first signal and second signal mixed therein, an estimate value of the first signal in the past is obtained as a first estimate value, and an estimate value of the second signal in the past is obtained as a second estimate value. Then, a first isolation signal is generated by subtracting the second estimate value from the first mixed signal, and a second isolation signal is generated by subtracting the first estimate value from the second mixed signal. Then, the signal generated using the first isolation signal and the second isolation signal is outputted as the first signal.

PATENT DESCRIPTION
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/JP2010/067121 filed Sep. 30, 2012, claiming priority based on Japanese Patent Application No. 2009-229509. filed Oct. 1, 2009, the contents of all of which arc incorporated herein by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to a signal processing technique for extracting a desired signal from a mixed signal in which a plurality of signals are mixed. 
     BACKGROUND ART 
     There are signal processing techniques for extracting a desired signal from a plurality of mixed signals. For example, a noise canceller (noise eliminating system) is a system for eliminating a noise superimposed over a desired voice signal (referred to hereinbelow as a desired signal). NPL 1 discloses a method of eliminating a noise using an adaptive filter. The method eliminates a noise by using an adaptive filter to estimate properties of an acoustic channel from a noise source to a microphone, processing a signal having a correlation with a noise (referred to hereinbelow as a noise-correlated signal) by the adaptive filter to produce a pseudo noise, and subtracting the pseudo noise from a mixed signal over which a noise is superimposed. 
     According to the technique disclosed in NPL 1, a desired signal component, sometimes referred to as crosstalk, may leak into the noise-correlated signal, and when a pseudo noise is produced using the noise-correlated signal having a crosstalk, part of an output signal is subtracted to cause distortion in the output signal. As a configuration for preventing such distortion, a cross-coupled noise canceller is disclosed in NPL 2, in which an adaptive filter capable of handling a crosstalk is installed to produce a pseudo crosstalk so that the noise and crosstalk are eliminated at the same time. 
     The “cross-coupled noise canceller” disclosed in NPL 2 will now be explained with reference to  FIG. 10 . A desired signal s 1 (k) from a desired signal source  910  can be assumed to be convolved with an impulse response h 11  (a transfer function H 11 ) of an acoustic space from the desired signal source  910  to a microphone  901  before the signal s 1 (k) reaches the microphone  901 . On the other hand, a noise s 2 (k) from the noise source  920  can also be assumed to be convolved with an impulse response h 21  (a transfer function H 21 ) of an acoustic space from the noise source  920  to the microphone  901  before the noise s 2 (k) reaches the microphone  901 . Therefore, a voice signal x 1 (k) output from the microphone  901  at a time k is a mixed signal expressed by EQ. (1) below. 
     Similarly, the desired signal s 1 (k) from the desired signal source  910  can be assumed to be convolved with an impulse response h 12  (a transfer function H 12 ) of an acoustic space from the desired signal source  910  to a microphone  902  before the signal s 1 (k) reaches the microphone  902 . On the other hand, the noise s 2 (k) from the noise source  920  can also be assumed to be convolved with an impulse response h 22  (a transfer function H 22 ) of an acoustic space from the noise source  920  to the microphone  902  before the noise s 2 (k) reaches the microphone  902 . Therefore, a voice signal x 2 (k) output from the microphone  902  at the time k is a mixed signal expressed by EQ. (2) below. 
     
       
         
           
             
               
                 
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     In these equations, h 11 (j), h 12 (j), h 21 (j), h 22 (j) correspond to the transfer functions H 11 , H 12 , H 21 , H 22  each representing an impulse response at a sample index j. M1, M2, N1, N2 each represent the length of the impulse response in the mixing process, which is the number of taps in transforming the transfer functions H 11 , H 12 , H 21 , H 22  into a filter. M1, M2, N1, N2 are related to the distances from the desired signal source  910  to the microphone  901 , from the noise source  920  to the microphone  902 , from the noise source  920  to the microphone  901 , and from the desired signal source  910  to the microphone  902 , and acoustic properties of the space, etc. 
     Especially, when the microphone  901  lies sufficiently close to the desired signal source  910 , M1−1=0 and h 11 (0)=1, so that EQ. (1) can be rewritten into EQ. (3) below. 
     
       
         
           
             
               
                 
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     Similarly, when the microphone  902  lies sufficiently close to the noise source  920 , M2−1=0 and h 22 (0)=1, so that EQ. (2) can be rewritten into EQ. (4) below. 
     
       
         
           
             
               
                 
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     At that time, an output y 1 (k) of a subtractor  903  is a signal obtained by subtracting an output u 1 (k) of an adaptive filter  907  from the signal x 1 (k) of the microphone  901 , as expressed by EQ. (5) below. On the other hand, y 2 (k) is signal obtained by subtracting an output u 2 (k) of an adaptive filter  908  from the signal x 2 (k) of the microphone  902 , as expressed by EQ. (6) below. In these equations, w 21,j (k), w 12,j (k) are coefficients of the adaptive filters  907 ,  908 . 
     
       
         
           
             
               
                 
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     That is, the output u 1 (k) of the adaptive filter  907  is a pseudo noise, and the output u 2 (k) of the adaptive filter  908  is a pseudo crosstalk. Ultimately, y 1 (k) is output as a signal whose noise is eliminated at the noise canceller. 
     From the above EQs. (3) and (5), the noise-free signal output y 1 (k) is given by the following equation. 
     
       
         
           
             
               
                 
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     That is, y 1 (k)=s 1 (k) stands when y 2 (k)=s 2 (k) and w 21,j (k)=h 21 (j), (j=0, 1, 2, . . . , N1−1), where perfect noise elimination can be achieved. 
     On the other hand, a system that can separate two signals in a similar configuration to that shown in  FIG. 10  is disclosed in NPL 3 (a feed-back blind signal separation system). The feed-back blind signal separation system disclosed in NPL 3 will now be described with reference to  FIG. 11 .  FIG. 11  is different from  FIG. 10  in that the output y 2 (k) of the subtractor  904  is output as one of the extracted signals. Moreover, coefficients for adaptive filters  917 ,  918  are updated using y 1 (k) and y 2 (k) at a coefficient updating section  981 . 
     In the blind signal separation system shown in  FIG. 11 , again, EQ. (7) stands when the microphones  901  and  902  lie sufficiently close to a first signal source  910  and a second signal source  930 , respectively. Likewise, EQ. (8) below stands for y 2 (k). 
     
       
         
           
             
               
                 
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     Since perfect signal separation is achieved only when y 1 (k)=s 1 (k) and y 2 (k)=s 2 (k) stand, the following two equations should stand as a requirement therefor.
 
 w   21,j ( k )= h   21 ( j ),  j= 0, 1, 2, . . . ,  N 1−1
 
 w   12,j ( k )= h   12 ( j ),  j= 0, 1, 2, . . . ,  N 2−1
 
     NPL 3 addresses a general case in which a condition that the microphone  901  and microphone  902  should lie sufficiently close to the first signal source  910  and second signal source  930  is not satisfied, and provides a requirement that the following equations should stand for perfectly separating signals.
 
 w   21,j ( k )= h   21 ( j )/ h   22 ( j ),  j= 0, 1, 2, . . . ,  N 1−1
 
 w   12,j ( k )= h   12 ( j )/ h   11 ( j ),  j= 0, 1, 2, . . . ,  N 2−1
 
     CITATION LIST 
     Non Patent Literature 
     NPL 1: B. Widrow, “Adaptive Noise Cancelling: Principles and Applications,” Proceedings of the IEEE, vol. 63, pp. 1692-1716, December 1975 
     NPL 2: M. J. Al-Kindi and J. Dunlop, “A low distortion adaptive noise cancellation structure for real time applications,” Proceedings of ICASSP 1987, vol. 12, pp. 2153-2156, April 1987 
     NPL 3: K. Nakayama, A. Horita and A. Hirano, “Effects of propagation delays and sampling rate on feed-back BSS and comparative studies with feed-forward BSS,” Proceedings of EUSIPCO 2008, 16 th  European Signal Processing Conference, Lausanne, Switzerland, CD-ROM, September 2008 
     SUMMARY OF INVENTION 
     Technical Problem 
     In the configurations disclosed in NPLs 2 to 3 above, however, to extract a desired signal from a mixed signal, current values (values at time k) of “other output signals” output as other signals (signals other than the desired signal) contained in the mixed signal are theoretically required. On the other hand, to determine the current values of the “other output signals,” a current value of the “desired output signal” output as the desired signal is required, thus posing a problem of reciprocity. Accordingly, coefficients (w 12,0 (k) and w 21,0 (k) in the example shown in  FIG. 11 ) corresponding to the current values of other output signals are set to zero in the filter to ignore them. Therefore, a desired signal may not successfully be extracted with accuracy, leading to degradation of quality of extracted output signals. 
     As such, an object of the present invention is to provide a signal processing technique to solve the aforementioned problem. 
     Solution to Problem 
     To attain the object described above, a signal processing method according to the present invention for extracting a first signal from a first mixed signal and a second mixed signal in which the first signal and a second signal are mixed, is characterized in comprising: determining an estimated value of said first signal in the past as a first estimated value; determining an estimated value of said second signal in the past as a second estimated value; removing said second estimated value from said first mixed signal to produce a first separated signal; removing said first estimated value from said second mixed signal to produce a second separated signal; and outputting a signal produced using said first separated signal and said second separated signal as said first signal. 
     To attain the object described above, another signal processing method according to the present invention for extracting a first signal using first to n-th mixed signals in which n signals from the first signal to an n-th signal are mixed, is characterized in comprising: for each natural number m from 1 to n, determining estimated values of the first to n-th signals in the past other than an m-th signal in the past, and removing the estimated values from an m-th mixed signal to produce an m-th separated signal; and producing a signal using said first to n-th separated signals, and outputting the signal as said first signal. 
     To attain the object described above, a signal processing apparatus according to the present invention is characterized in comprising: a first filter for producing, from a first mixed signal generated to have a first signal and a second signal mixed, an estimated value of said second signal in the past as a second estimated value; a first subtracting section for removing said second estimated value from said first mixed signal to produce a first separated signal; a second filter for producing, from a second mixed signal generated to have the first signal and second signal mixed, an estimated value of said first signal in the past as a first estimated value; a second subtracting section for removing said first estimated value from said second mixed signal to produce a second separated signal; and an output section for outputting a signal produced using said first separated signal and said second separated signal as said first signal. 
     To attain the object described above, another signal processing apparatus according to the present invention is characterized in comprising: a filter for, for each natural number m from 1 to n, producing, from first to n-th mixed signals generated to have n signals from a first signal to an n-th signal mixed, estimated values of the first to n-th signals in the past other than an m-th signal in the past; a subtracting section for removing said estimated values from said first to n-th mixed signals to produce first to n-th separated signals; and an output section for outputting a signal produced using said first to n-th separated signals as said first signal. 
     To attain the object described above, a signal processing program according to the present invention causes a computer to execute: for extracting a first signal from a first mixed signal and a second mixed signal in which the first signal and a second signal are mixed, processing of determining an estimated value of said first signal in the past as a first estimated value; processing of determining an estimated value of said second signal in the past as a second estimated value; processing of removing said second estimated value from said first mixed signal to produce a first separated signal; processing of removing said first estimated value from said second mixed signal to produce a second separated signal; and processing of outputting a signal produced using said first separated signal and said second separated signal as said first signal. 
     To attain the object described above, another signal processing program according to the present invention causes a computer to execute: for extracting a first signal using first to n-th mixed signals in which n signals from the first signal to an n-th signal are mixed, processing of, for each natural number m from 1 to n, determining estimated values of the first to n-th signals in the past other than an m-th signal in the past, and removing a sum of the estimated values from said m-th mixed signal to produce an m-th separated signal; and processing of producing a signal using said first to n-th separated signals, and outputting the signal as said first signal. 
     Advantageous Effects of Invention 
     According to the present invention, a desired signal can be extracted with higher accuracy from a mixed signal in which a plurality of signals are mixed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       [ FIG. 1 ] A block diagram showing a first embodiment of the present invention. 
       [ FIG. 2 ] A block diagram showing a configuration of a filter included in  FIG. 1 . 
       [ FIG. 3 ] A block diagram showing a configuration of a current component separating section included in  FIG. 1 . 
       [ FIG. 4 ] A block diagram showing a second embodiment of the present invention. 
       [ FIG. 5 ] A block diagram showing a configuration of an adaptive filter included in  FIG. 4 . 
       [ FIG. 6 ] A block diagram showing a configuration of a current component separating section included in  FIG. 4 . 
       [ FIG. 7 ] A block diagram showing a third embodiment of the present invention. 
       [ FIG. 8 ] A block diagram showing a fourth embodiment of the present invention. 
       [ FIG. 9 ] A block diagram showing another embodiment of the present invention. 
       [ FIG. 10 ] A block diagram showing a configuration of a conventional noise canceller. 
       [ FIG. 11 ] A block diagram showing a configuration of a conventional feed-back blind signal separation system for two inputs. 
       [ FIG. 12 ] A block diagram showing a configuration of a feed-back blind signal separation system for three inputs. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Several embodiments of the present invention will now be described in detail with reference to the accompanying drawings by way of illustration. It should be noted that components described in the embodiments below are provided only by way of example, and it is not intended to limit the technical scope of the present invention thereto. 
     First Embodiment 
       FIG. 1  is a block diagram showing a configuration of a signal processing apparatus  100  in accordance with a first embodiment of the present invention. The description here will address a case in which signals s 1 (k), s 2 (k) from two sources are separated as an example. A first mixed signal x 1 (k) output from a microphone  1  and a second mixed signal x 2 (k) output from a microphone  2  are supplied to a past component separating section  20  at subtractors  3 ,  4 , respectively, that serve as first, second subtracting sections. A filter  10  supplies a first estimated value (EQ. (9)) of a component based on a second output signal in the past to the subtractor  3 , and a filter  12  supplies a second estimated value (EQ. (10)) of a component based on a first output signal in the past to the subtractor  4 . As used herein, “current” refers to a time at k, and “past” refers to a time preceding the time k. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         u 
                         ~ 
                       
                       1 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       
                         
                           N 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
                           w 
                           21 
                         
                         ⁡ 
                         
                           ( 
                           j 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           y 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             j 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     10 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         u 
                         ~ 
                       
                       2 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       
                         
                           N 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
                           w 
                           12 
                         
                         ⁡ 
                         
                           ( 
                           j 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           y 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           
                             k 
                             - 
                             j 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
           
         
       
     
     In EQs. (9) and (10), the total sum on the right side is calculated starting with j=1, rather than j=0. That is, inputs to the filter  10  and filter  12  are y 2 (k−1), y 2 (k−2), . . . , y 2 (k−N1+1) and y 1 (k−1), y 1 (k−2), . . . , y 1 (k−N1+1). 
     The subtractor  3  subtracts an output of the filter  10  from the first mixed signal x 1 (k), produces a first separated signal y′ 1 (k) as a result, and passes it to a current component separating section  5 . The subtractor  4  subtracts an output of the filter  12  from the second mixed signal x 2 (k), produces a second separated signal y′ 2 (k) as a result, and passes it to the current component separating section  5 . The first separated signal y′ 1 (k) and second separated signal y′ 2 (k) are used to determine a first output signal and a second output signal as y 1 (k), y 2 (k), which are transmitted to output terminals  6  and  7 , respectively. That is, the current component separating section  5  functions as an output section for outputting a signal produced using the first separated signal and second separated signal as the first signal from the signal source. 
     The second output signal y 2 (k) is supplied to a delay element  9 . Similarly, the first output signal y 1 (k) is supplied to a delay element  11 . The delay element  9  and delay element  11  delay the input first, second output signals by one sample, and supply them to the filter  10  and filter  12 , respectively. That is, signals supplied to the filter  10  and filter  12  are the second output signal in the past and the first output signal in the past, respectively. 
       FIG. 2( a )  is an exemplary configuration of the filter  10 . The filter  10  is supplied with a second output signal in the past y 2 (k−1). The second output signal in the past y 2 (k−1) is transmitted to a multiplier  102   1  and a delay element  103   2  in the filter  10 . The multiplier  102   1  multiplies y 2 (k−1) by a factor of w 21 (1) to result in w 21 (1)·y 2 (k−1), which is transmitted to an adder  101   2 . The delay element  103   2  delays y 2 (k−1) by one sample to result in y 2 (k−2), which is transmitted to a multiplier  102   2  and a delay element  103   3 . The multiplier  102   2  multiplies y 2 (k−2) by a factor of w 21 (2) to result in w 21 (2)·y 2 (k−2), which is transmitted to an adder  101   2 . The adder  101   2  adds w 21 (1)·y 2 (k−1) and w 21 (2)·y 2 (k−2), and transmits a result to an adder  101   3 . Thereafter, such a process is repeated by a series of delay elements and multipliers and finally an adder  101   N1−1  outputs a total value as an estimated value represented by EQ. (9) given above. The method comprising the series of operations is known as convolution. 
     On the other hand,  FIG. 2( b )  shows an exemplary configuration of the filter  12 . The configuration and operation of the filter  12  can be represented by merely replacing the input signal y 2 (k−1) with y 1 (k−1), and coefficients w 21 (j) (j=1, 2, . . . , N1−1) of the multipliers  122   1 - 122   N2−1  with w 12 (j) (j=1, 2, . . . , N2−1). The other components and operations of the filter  12  are similar to those of the filter  10 . Specifically, the filter  12  comprises delay elements  123   2 - 103   N2−1  corresponding to the delay elements  103   2 - 103   N1−1 . The filter  12  also comprises multipliers  122   1 - 122   N2−1  corresponding to the multipliers  102   1 - 102   N1−1 . It moreover comprises adders  121   2 - 101   N2−1  corresponding to  101   2 - 101   N1−1 . Therefore, detailed description of each of them will be omitted here. It should be noted that the coefficients w 21 (j) (j=1, 2, . . . , N1−1), w 12 (j) (j=1, 2, . . . , N2−1) in the filters  10 ,  12  are constants, rather than functions of time k. Thus, when the transfer functions H 11 , H 12 , H 21 , H 22  of the mixed signal generation process do not vary with time, the circuit and/or software for implementing the present embodiment can be significantly simplified. 
     The filter  10  and filter  12  are supplied with the second output signal in the past y 2 (k−1) and the first output signal in the past y 1 (k−1) delayed from the second output signal y 2 (k) and first output signal y 1 (k) by one sample by the delay element  9  and delay element  11 , respectively. The filter  10  is therefore designed to calculate a component of the second signal s 2 (k) in the past that is assumed to be mixed with the first mixed signal x 1 (k), as the first estimated value (EQ. (9)). On the other hand, the filter  12  is designed to calculate a component of the first signal s 1 (k) in the past that is assumed to be mixed with the second mixed signal x 2 (k), as the second estimated value (EQ. (10)). 
       FIG. 3  is a diagram showing an internal configuration of the current component separating section  5 . The output of the subtractor  3  is supplied to a multiplier  51  and a multiplier  53 . The output of the subtractor  4  is supplied to a multiplier  52  and a multiplier  54 . The multiplier  51  multiplies the input by a factor of v 11  and supplies the result to an adder  55 . The multiplier  54  multiplies the input by a factor of v 21  and supplies the result to the adder  55 . The adder  55  adds them together and outputs resulting y 1 (k) as follows:
 
[Equation 11]
 
 y   2 ( k )= v   12   {x   1 ( k )− ũ   1 ( k )}+ v   21   {x   2 ( k )− ũ   2 ( k )}  (11)
 
     On the other hand, the multiplier  52  multiplies the input by a factor of v 22  and supplies the result to an adder  56 . The multiplier  53  multiplies the input by a factor of v 12  and supplies the result to the adder  56 . The adder  56  adds them together and outputs resulting y 2 (k) as follows:
 
[Equation 12]
 
 y   2 ( k )= v   12   {x   1 ( k )− ũ   1 ( k )}+ v   22   {x   2 ( k )− ũ   2 ( k )}  (12)
 
     The results y 1 (k) and y 2 (k) are outputs of the current component separating section  5 . EQ. (11) and EQ. (12) may be combined together as a matrix as given by EQ. (13). 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               v 
                               11 
                             
                           
                           
                             
                               v 
                               21 
                             
                           
                         
                         
                           
                             
                               v 
                               12 
                             
                           
                           
                             
                               v 
                               22 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     Consequently, the past component separating section  20  in  FIG. 1  comprising the subtractors  3 ,  4 , filters  10 ,  12 , and delay elements  9 ,  11  uses output signals in the past y 1 (k−j), y 2 (k−j) (j&gt;0) to separate out past components present in the mixed signals. A result thereof is supplied to the current component separating section  5 , which further separates a current component. 
     In other words, the past component separating section  20  uses the first mixed signal x 1 (k) and the second output signals in the past y 2 (k−1), y 2 (k−2), . . . , y 2 (k−N1+1) to produce the first separated signal y′ 1 (k). It also uses the second mixed signal x 2 (k) and the first signals in the past y 1 (k−1), y 1 (k−2), . . . , y 1 (k−N1+1) to produce the second separated signal y′ 2 (k). 
     The current component separating section  5  is supplied with the first separated signal y′ 1 (k) and second separated signal y′ 2 (k), and produces the first output signal y 1 (k) and second output signal y 2 (k). That is, the first separated signal and second separated signal are used to produce a first output signal. Particularly, an estimated value of a current (time k) second signal is determined as a third estimated value using the second separated signal, removes the third estimated value from the first separated signal to produce the first output signal. The third estimated value is a component of the current (time k) second signal estimated to be mixed with the first mixed signal. 
     Now a confirmation will be made that in the configuration shown in.  FIG. 1 , the first output signal y 1 (k) and second output signal y 2 (k) resulting from separation from the first mixed signal x 1 (k) and second mixed signal x 2 (k) correspond to the first signal s 1 (k) and second signal s 2 (k) before mixture. 
     Representing the right side of EQs. (5) and (6) by a term based on the current first output signal y 1 (k) and second output signal y 2 (k) separated from a term based on the other factors, the following equations are obtained: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       14 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           x 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             w 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           
                             
                               N 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             
                               w 
                               21 
                             
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 - 
                                 j 
                               
                               ) 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           x 
                           1 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             u 
                             ~ 
                           
                           1 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             w 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       15 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           x 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             w 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                       - 
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             1 
                           
                           
                             
                               N 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                             - 
                             1 
                           
                         
                         ⁢ 
                         
                           
                             
                               w 
                               12 
                             
                             ⁡ 
                             
                               ( 
                               j 
                               ) 
                             
                           
                           ⁢ 
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               
                                 k 
                                 - 
                                 j 
                               
                               ) 
                             
                           
                         
                       
                     
                     = 
                     
                       
                         
                           x 
                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             u 
                             ~ 
                           
                           2 
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       - 
                       
                         
                           
                             w 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             0 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     Combining EQs. (14) and (15) together into a matrix format, EQ. (16) is obtained as follows: 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     16 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     - 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   w 
                                   21 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   w 
                                   12 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     Rewriting this equation, EQ. (17) is obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     17 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     - 
                     
                       
                         [ 
                         
                           
                             
                               0 
                             
                             
                               
                                 
                                   w 
                                   21 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   w 
                                   12 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   0 
                                   ) 
                                 
                               
                             
                             
                               0 
                             
                           
                         
                         ] 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             
                               
                                 
                                   y 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   y 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Reorganization of the equation in terms of y 1 (k), y 2 (k) gives the following equation: 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     18 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               
                                 w 
                                 21 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 w 
                                 12 
                               
                               ⁡ 
                               
                                 ( 
                                 0 
                                 ) 
                               
                             
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 y 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 x 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Solving the equation for y 1 (k), y 2 (k), the following equations are obtained: 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     19 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                   
                                     
                                       
                                         w 
                                         21 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         0 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         w 
                                         12 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         0 
                                         ) 
                                       
                                     
                                   
                                   
                                     1 
                                   
                                 
                               
                               ] 
                             
                             
                               - 
                               1 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         x 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         x 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               1 
                               
                                 Δ 
                                 2 
                               
                             
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                   
                                     
                                       - 
                                       
                                         
                                           w 
                                           21 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           0 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       - 
                                       
                                         
                                           w 
                                           12 
                                         
                                         ⁡ 
                                         
                                           ( 
                                           0 
                                           ) 
                                         
                                       
                                     
                                   
                                   
                                     1 
                                   
                                 
                               
                               ] 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         x 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         x 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     20 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Δ 
                     2 
                   
                   = 
                   
                     1 
                     - 
                     
                       
                         
                           w 
                           12 
                         
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           21 
                         
                         ⁡ 
                         
                           ( 
                           0 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   20 
                   ) 
                 
               
             
           
         
       
     
     Now a new square matrix v is defined as EQ. (21), and then, EQ. (19) can be rewritten into EQ. (22) below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     21 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   v 
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               v 
                               11 
                             
                           
                           
                             
                               v 
                               12 
                             
                           
                         
                         
                           
                             
                               v 
                               21 
                             
                           
                           
                             
                               v 
                               22 
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       [ 
                       
                         
                           
                             
                               1 
                               
                                 Δ 
                                 2 
                               
                             
                           
                           
                             
                               
                                 - 
                                 
                                   
                                     w 
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     0 
                                     ) 
                                   
                                 
                               
                               
                                 Δ 
                                 2 
                               
                             
                           
                         
                         
                           
                             
                               
                                 - 
                                 
                                   
                                     w 
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     0 
                                     ) 
                                   
                                 
                               
                               
                                 Δ 
                                 2 
                               
                             
                           
                           
                             
                               1 
                               
                                 Δ 
                                 2 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     22 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               v 
                               11 
                             
                           
                           
                             
                               v 
                               21 
                             
                           
                         
                         
                           
                             
                               v 
                               12 
                             
                           
                           
                             
                               v 
                               22 
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     Since EQ. (22) is identical to EQ. (13), the first, second output signals can be obtained in the present embodiment as in EQs. (7) and (8). Specifically, under a condition that the following two equations stand, the first output signal y 1 (k) corresponds to the current first signal s 1 (k) generated from the first signal source and mixed with the first mixed signal.
 
 w   21 ( j )= h   21 ( j )/ h   22 ( j ),  j= 0, 1, 2, . . . ,  N 1−1
 
 w   12 ( j )= h   12 ( j )/ h   11 ( j ),  j= 0, 1, 2, . . . ,  N 2−1
 
     As described above, since a condition that w 21 (0)=0 and w 12 (0)=0 is not imposed in this embodiment, signal separation can be achieved for arbitrary coefficients w 21 (0) and w 12 (0) with high accuracy. That is, a desired signal can be extracted with higher accuracy from a mixed signal in which a plurality of signals are mixed. 
     Second Embodiment 
       FIG. 4  is a block diagram showing a configuration of a signal processing apparatus  200  in accordance with a second embodiment of the present invention. The present embodiment has a similar configuration to that of the first embodiment, except that the past component separating section  20  is replaced with a past component separating section  21 , the current component separating section  5  is replaced with a current component separating section  50 , the filters  10 ,  12  are replaced with adaptive filters  40 ,  42 , and a coefficient adaptation section  8  is added. Therefore, similar components are designated by similar reference numerals and explanation thereof will be omitted. 
     The coefficient adaptation section  8  produces coefficient updating information for updating coefficients used in the past component separating section  21  and current component separating section  50  in response to the output signals y 1 (k), y 2 (k). The produced coefficient updating information is supplied to the adaptive filters  40 ,  42 , and current component separating section  50 . The coefficient adaptation section  8  is capable of producing the coefficient updating information using a variety of coefficient adaptation algorithms. In a case that a normalized LMS algorithm is used, the coefficients w 21,j (k), w 12,j (k) are updated according to the equations below. It should be noted that while the coefficients w 21,j , w 12,j  have the same meaning as that of w 21 (j), w 21 (j) in the first embodiment, the designation as w 21,j (k), w 12,j (k) are used in the present embodiment because these coefficients are dependent upon time k. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     23 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             w 
                             
                               21 
                               , 
                               j 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               w 
                               
                                 21 
                                 , 
                                 j 
                               
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             μ 
                             ⁢ 
                             
                               
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 δ 
                                 + 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       0 
                                     
                                     
                                       
                                         N 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         1 
                                       
                                       - 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       y 
                                       2 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         k 
                                         - 
                                         l 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               w 
                               
                                 21 
                                 , 
                                 j 
                               
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             μ 
                             ⁢ 
                             
                               
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   σ 
                                   
                                     y 
                                     2 
                                   
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             w 
                             
                               12 
                               , 
                               j 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               + 
                               1 
                             
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               w 
                               
                                 12 
                                 , 
                                 j 
                               
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             μ 
                             ⁢ 
                             
                               
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 δ 
                                 + 
                                 
                                   
                                     ∑ 
                                     
                                       l 
                                       = 
                                       0 
                                     
                                     
                                       
                                         N 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         2 
                                       
                                       - 
                                       1 
                                     
                                   
                                   ⁢ 
                                   
                                     
                                       y 
                                       1 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         k 
                                         - 
                                         l 
                                       
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               w 
                               
                                 12 
                                 , 
                                 j 
                               
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           + 
                           
                             μ 
                             ⁢ 
                             
                               
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       k 
                                       - 
                                       j 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 
                                   σ 
                                   
                                     y 
                                     1 
                                   
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     In these equations, the constant μ represents a step size, and 0&lt;μ&lt;1. Moreover, δ is a small constant for avoiding division by zero. The second term on the right side of EQ. (23) designates an amount of the coefficient to be updated, which is supplied to the current component separating section  50  when j=0, and to the adaptive filter  40  when j&gt;0. Similarly, the second term on the right side of EQ. (24) is supplied to the current component separating section  50  when j=0, and to the adaptive filter  42  when j&gt;0. That is, the coefficients of the adaptive filters  40 ,  42  are updated using a correlation (correlation value) between y 1 (k) and y 2 (k). Thus, a gradient coefficient updating algorithm, represented by the normalized LMS algorithm, is used to update the coefficient w 21,j (k) of the filter  40  based on the output signal y 1 (k) and modify the coefficient w 12,j (k) of the filter  42  based on the output signal y 2 (k), whereby output signals can be obtained with high accuracy even when the transfer functions H 11 , H 12 , H 21 , H 22  of the mixed signal generation process vary with time depending upon a change in an external environment. 
       FIG. 5  shows an exemplary configuration of the adaptive filter  40  and adaptive filter  42 . The adaptive filter  40  and adaptive filter  42  in  FIG. 5  are similar to the filters  10  and  12  in  FIG. 2 , except that the amount of the coefficient to be updated is supplied to multipliers  402   1 ,  402   2 , . . . ,  402   N1−1  and multipliers  422   1 ,  422   2 , . . . ,  422   N2−1 . The amount of the coefficient to be updated μy 1 (k)y 2 (k−j)/σ 2 y 2  (j=1, 2, . . . , N1−1) supplied by the coefficient adaptation section  8  is supplied to the multipliers  402   1 ,  402   2 , . . . ,  402   N1−1  for use in coefficient updating according to EQ. (23). Similarly, the amount of the coefficient to be updated μy 2 (k)y 1 (k−j)/σ 2 y 1  (j=1, 2, . . . , N2−1) supplied by the coefficient adaptation section  8  is supplied to the multipliers  422   1 ,  422   2 , . . . ,  422   N2−1  for use in coefficient updating according to EQ. (24). Moreover, the amounts of coefficient updating μy 1 (k)y 2 (k)/σ 2 y 2  and μy 2 (k)y 1 (k)/σ 2 y 1  corresponding to j=0 are supplied to the current component separating section  50 . 
       FIG. 6  is a diagram showing an exemplary configuration of the current component separating section  50 . It is different from the current component separating section  5  shown in  FIG. 3  in that the multipliers  501 ,  502 ,  503 ,  504  are supplied with coefficient updating information. The multipliers  501 ,  503  are supplied with μy 1 (k)y 2 (k)/σ 2 y 2 , which is used to perform coefficient updating according to EQ. (23). Moreover, the multipliers  502 ,  503  are supplied with μy 2 (k)y 1 (k)/σ 2 y 1 , which is used to perform coefficient updating according to EQ. (24). 
     The coefficient updating algorithm as applied herein may be one expressed by EQs. (25) and (26) below.
 
[Equation 25]
 
 w   21,j ( k+ 1)= w   21,j ( k )+μ·ƒ{α· y   1 ( k )}· g{β·y   2 ( k−j )}  (25)
 
[Equation 26]
 
 w   12,j ( k+ 1)= w   12,j ( k )+μ·ƒ{α· y   2 ( k )}· g{β·y   1 ( k−j )}  (26)
 
     In these equations, f{·} and g{·} are odd functions, and α, β are constants. For f{·} and g{·}, a sigmoid function, hyperbolic tangent (tan h) or the like may be used. Since the other operations including coefficient updating are similar to those using EQs. (23) and (24), details thereof will be omitted. Thus, the correlation between the plurality of output signals y 1 (k), y 2 (k) can be used to modify coefficients w 21,j (k), w 12,j (k) of the filters  40 ,  42 , whereby output signals can be obtained with high accuracy even when the transfer functions H 11 , H 12 , H 21 , H 22  of the mixed signal generation process vary with time depending upon a change in an external environment. 
     According to the present embodiment as described above, coefficients used in the adaptive filters  40 ,  42  and current component separating section  50  may be updated depending upon an output signal, which enables signal separation to be achieved with higher accuracy corresponding to a change in an external environment. 
     Third Embodiment 
     &lt;Configuration as an Underlying Technique&gt; 
     Before explaining a third embodiment of the present invention, its underlying technique will be described with reference to  FIG. 12 .  FIG. 12  shows the technique disclosed in NPL 2 extended to a number of microphones of three. This system comprises microphones  801 - 803 , and output terminals  807 - 809 . For an acoustic space from a first signal source  810  to the microphones  801 - 803 , an impulse response h 11  (a transfer function H 11 ), an impulse response h 12  (a transfer function H 12 ), and an impulse response h 13  (a transfer function H 13 ) are defined. Similarly, for an acoustic space from a second signal source  820  to the microphones  801 - 803 , an impulse response h 21  (a transfer function H 21 ), an impulse response h 22  (a transfer function H 22 ), and an impulse response h 23  (a transfer function H 23 ) are defined. Moreover, for an acoustic space from a third signal source  830  to the microphones  801 - 803 , an impulse response h 31  (a transfer function H 31 ), an impulse response h 32  (a transfer function H 32 ), and an impulse response h 33  (a transfer function H 33 ) are defined. 
     On the other hand, the signal processing apparatus side comprises adaptive filters  811 - 816  corresponding to these impulse responses. The adaptive filter  811  supplies an output to a subtractor  804  in response to a second output y 2 (k). The adaptive filter  812  supplies an output to the subtractor  804  in response to a third output y 3 (k). The adaptive filter  813  supplies an output to a subtractor  805  in response to a first output y 1 (k). The adaptive filter  814  supplies an output to the subtractor  805  in response to the third output y 3 (k). The adaptive filter  815  supplies an output to a subtractor  806  in response to the second output y 2 (k). The adaptive filter  816  supplies an output to the subtractor  806  in response to the first output y 1 (k). Again, coefficients of these adaptive filters are updated as appropriate using the first to third outputs. 
     The microphone signals x 1 (k), x 2 (k), x 3 (k) are expressed by the following equations when these microphones  801 - 803  lie sufficiently close to the first, second, third signal sources  810 ,  820 ,  830 . 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     27 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         s 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             31 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   27 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     28 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         s 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             32 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   28 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     29 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       x 
                       3 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             13 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             23 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         s 
                         3 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   29 
                   ) 
                 
               
             
           
         
       
     
     Similarly to  FIG. 10 , the output signals y 1 (k), y 2 (k), y 3 (k) are expressed by the following equations: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       30 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       1 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         s 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             21 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             31 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             w 
                             
                               21 
                               , 
                               j 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             3 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             w 
                             
                               31 
                               , 
                               j 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   30 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       31 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       2 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         s 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             12 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             32 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             21 
                             , 
                             j 
                           
                         
                         ⁢ 
                         
                           ( 
                           k 
                           ) 
                         
                         ⁢ 
                         
                           
                             y 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             4 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             w 
                             
                               32 
                               , 
                               j 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   31 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       32 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       y 
                       3 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         s 
                         3 
                       
                       ⁡ 
                       
                         ( 
                         k 
                         ) 
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             13 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     + 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             h 
                             23 
                           
                           ⁡ 
                           
                             ( 
                             j 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             s 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             13 
                             , 
                             j 
                           
                         
                         ⁢ 
                         
                           ( 
                           k 
                           ) 
                         
                         ⁢ 
                         
                           
                             y 
                             1 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                     - 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           0 
                         
                         
                           
                             N 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             w 
                             
                               23 
                               , 
                               j 
                             
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         ⁢ 
                         
                           
                             y 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               k 
                               - 
                               j 
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   32 
                   ) 
                 
               
             
           
         
       
     
     Therefore, the following conditions should be satisfied for signal separation.
 
 w   21,j ( k )= h   21 ( j ),  j= 0, 1, 2, . . . ,  N 1−1
 
 w   12,j ( k )= h   12 ( j ),  j= 0, 1, 2, . . . ,  N 2−1
 
 w   31,j ( k )= h   31 ( j ),  j= 0, 1, 2, . . . ,  N 3−1
 
 w   32,j ( k )= h   32 ( j ),  j= 0, 1, 2, . . . ,  N 4−1
 
 w   13,j ( k )= h   13 ( j ),  j= 0, 1, 2, . . . ,  N 5−1
 
 w   23,j ( k )= h   23 ( j ),  j= 0, 1, 2, . . . ,  N 6−1
 
     Moreover, in a general case in which the condition that the microphones  801 - 803  lie sufficiently close to the first, second, third signal sources  810 ,  820 ,  830  is not satisfied, signal separation is achieved provided the following equations stand.
 
 w   21,j ( k )= h   21 ( j )/ h   22 ( j ),  j= 0, 1, 2, . . . ,  N 1−1
 
 w   12,j ( k ) = h   12 ( j )/ h   11 ( j ),  j= 0, 1, 2, . . . ,  N 2−1
 
 w   31,j ( k )= h   31 ( j )/ h   33 ( j ),  j= 0, 1, 2, . . . ,  N 3−1
 
 w   32,j ( k )= h   32 ( j )/ h   33 ( j ),  j= 0, 1, 2, . . . ,  N 4−1
 
 w   13,j ( k )= h   13 ( j )/ h   11 ( j ),  j= 0, 1, 2, . . . ,  N 5−1
 
 w   23,j ( k )= h   23 ( j )/ h   22 ( j ),  j= 0, 1, 2, . . . ,  N 6−1
 
     Configuration According to the Present Embodiment 
     To extract a desired signal from a mixed signal, the underlying technique described above also theoretically requires current values of other signals (signals other than the desired signal) contained in the mixed signal. On the other hand, to determine the current values of the “other signals,” a current value of the desired signal is required, thus posing a problem of reciprocity. Accordingly, coefficients (w 12,0 (k), w 21,0 (k), w 31,0 (k), w 32,0 (k), w 13,0 (k), w 23,0 (k) in the example above) corresponding to the current values of other output signals are set to zero in the filter to ignore them. Therefore, a desired signal may not successfully be extracted with accuracy, leading to degradation of quality of extracted output signals. 
     Now the third embodiment of the present invention will be described in contrast thereto with reference to a block diagram shown in  FIG. 7 .  FIG. 7  corresponds to  FIG. 1 , added with a microphone to result in a total number of microphones of three. That is, it is a configuration for 3-channel signal separation. A difference from  FIG. 1  is in that a filter, a delay element, a subtractor, and an output terminal are added, and the current component separating section  5  is replaced with a current component separating section  650 . 
     The subtractor  611  is supplied with estimated values of components based on output signals in the past from filters  631 ,  632 . The subtractor  612  is supplied with estimated values of components based on output signals in the past from filters  633 ,  634 . The subtractor  613  is supplied with estimated values of components based on output signals in the past from filters  635 ,  636 . These estimated values are given by EQ. (33) below. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     33 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 u 
                                 ~ 
                               
                               12 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 
                                   N 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   w 
                                   
                                     12 
                                     , 
                                     j 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 u 
                                 ~ 
                               
                               21 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 
                                   N 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   w 
                                   
                                     21 
                                     , 
                                     j 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 u 
                                 ~ 
                               
                               31 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 
                                   N 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   3 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   w 
                                   
                                     31 
                                     , 
                                     j 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   3 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 u 
                                 ~ 
                               
                               32 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 
                                   N 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   4 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   w 
                                   
                                     32 
                                     , 
                                     j 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   3 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 u 
                                 ~ 
                               
                               13 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 N5 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   w 
                                   
                                     13 
                                     , 
                                     j 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 u 
                                 ~ 
                               
                               23 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                           = 
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               
                                 
                                   N 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   6 
                                 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               
                                 
                                   w 
                                   
                                     23 
                                     , 
                                     j 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               ⁢ 
                               
                                 
                                   y 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     k 
                                     - 
                                     j 
                                   
                                   ) 
                                 
                               
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   33 
                   ) 
                 
               
             
           
         
       
     
     The subtractors  611 ,  612 ,  613  subtract the estimated values as given by EQ. (33) from the first, second, third mixed signals x 1 (k), x 2 (k), x 3 (k) supplied by the microphones  601 ,  602 ,  603 , and pass results thereof to the current component separating section  650 . To clarify the operation of the current component separating section  650 , the operation is analyzed, as in the case of two signal separation shown in  FIG. 1 . 
     Following the case shown in  FIG. 1 , the equation below is obtained. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       34 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               3 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   21 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   31 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   12 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   32 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   3 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   13 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   23 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     - 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   
                                     w 
                                     
                                       21 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   
                                     w 
                                     
                                       31 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     3 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     w 
                                     
                                       12 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   
                                     w 
                                     
                                       32 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     3 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   
                                     w 
                                     
                                       13 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               + 
                               
                                 
                                   
                                     w 
                                     
                                       23 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ⁢ 
                       
                           
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   34 
                   ) 
                 
               
             
           
         
       
     
     Rewriting this equation, the equation below is obtained. 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       35 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               3 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                       
                     
                       
                         [ 
                         
                           
                             
                               
                                 
                                   
                                     x 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     31 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     x 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     32 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   
                                     x 
                                     3 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     13 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                                 - 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     23 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         ] 
                       
                       - 
                       
                         
                           [ 
                           
                             
                               
                                 0 
                               
                               
                                 
                                   
                                     w 
                                     
                                       21 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     w 
                                     
                                       31 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     w 
                                     
                                       12 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 0 
                               
                               
                                 
                                   
                                     w 
                                     
                                       32 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     w 
                                     
                                       13 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     w 
                                     
                                       23 
                                       , 
                                       0 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 0 
                               
                             
                           
                           ] 
                         
                         ⁢ 
                         
                             
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       y 
                                       1 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       y 
                                       3 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   35 
                   ) 
                 
               
             
           
         
       
     
     Reorganization of the equation in terms of y 1 (k), y 2 (k), y 3 (k) gives the following equation: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       36 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       [ 
                       
                         
                           
                             1 
                           
                           
                             
                               
                                 w 
                                 
                                   21 
                                   , 
                                   0 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 w 
                                 
                                   31 
                                   , 
                                   0 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 w 
                                 
                                   12 
                                   , 
                                   0 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             1 
                           
                           
                             
                               
                                 w 
                                 
                                   32 
                                   , 
                                   0 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 w 
                                 
                                   13 
                                   , 
                                   0 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 w 
                                 
                                   23 
                                   , 
                                   0 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             1 
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 y 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 y 
                                 3 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                   = 
                   
                     [ 
                     
                       
                         
                           
                             
                               
                                 x 
                                 1 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 21 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 31 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 2 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 12 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 32 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 x 
                                 3 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 13 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                             - 
                             
                               
                                 
                                   u 
                                   ~ 
                                 
                                 23 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   36 
                   ) 
                 
               
             
           
         
       
     
     Solving the equation for y 1 (k), y 2 (k), y 3 (k), the following equations are obtained: 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     37 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     y 
                                     1 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     y 
                                     2 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     y 
                                     3 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               [ 
                               
                                 
                                   
                                     1 
                                   
                                   
                                     
                                       
                                         w 
                                         
                                           21 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                   
                                     
                                       
                                         w 
                                         
                                           31 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         w 
                                         
                                           12 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                   
                                     1 
                                   
                                   
                                     
                                       
                                         w 
                                         
                                           32 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         w 
                                         
                                           13 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                   
                                     
                                       
                                         w 
                                         
                                           23 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                   
                                     1 
                                   
                                 
                               
                               ] 
                             
                             
                               - 
                               1 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     
                                       
                                         x 
                                         1 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         21 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         31 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         x 
                                         2 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         12 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         32 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         x 
                                         3 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         13 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                     - 
                                     
                                       
                                         
                                           u 
                                           ~ 
                                         
                                         23 
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             1 
                             
                               Δ 
                               3 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     1 
                                     - 
                                     
                                       
                                         
                                           w 
                                           
                                             32 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             23 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         
                                           w 
                                           
                                             31 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             23 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         w 
                                         
                                           21 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         
                                           w 
                                           
                                             21 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             32 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         w 
                                         
                                           31 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         
                                           w 
                                           
                                             32 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             13 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         w 
                                         
                                           12 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     1 
                                     - 
                                     
                                       
                                         
                                           w 
                                           
                                             31 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             13 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         
                                           w 
                                           
                                             31 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             12 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         w 
                                         
                                           32 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         
                                           w 
                                           
                                             12 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             23 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         w 
                                         
                                           13 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     
                                       
                                         
                                           w 
                                           
                                             21 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             13 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                     - 
                                     
                                       
                                         w 
                                         
                                           23 
                                           , 
                                           0 
                                         
                                       
                                       ⁡ 
                                       
                                         ( 
                                         k 
                                         ) 
                                       
                                     
                                   
                                 
                                 
                                   
                                     1 
                                     - 
                                     
                                       
                                         
                                           w 
                                           
                                             21 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                       ⁢ 
                                       
                                         
                                           w 
                                           
                                             12 
                                             , 
                                             0 
                                           
                                         
                                         ⁡ 
                                         
                                           ( 
                                           k 
                                           ) 
                                         
                                       
                                     
                                   
                                 
                               
                             
                             ] 
                           
                         
                       
                     
                   
                   
                     
                       
                           
                         ⁢ 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     
                                       x 
                                       1 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         u 
                                         ~ 
                                       
                                       21 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         u 
                                         ~ 
                                       
                                       31 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       x 
                                       2 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         u 
                                         ~ 
                                       
                                       12 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         u 
                                         ~ 
                                       
                                       32 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       x 
                                       3 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         u 
                                         ~ 
                                       
                                       13 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                   - 
                                   
                                     
                                       
                                         u 
                                         ~ 
                                       
                                       23 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       k 
                                       ) 
                                     
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   37 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     38 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     Δ 
                     3 
                   
                   = 
                   
                     1 
                     + 
                     
                       
                         
                           w 
                           
                             21 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             32 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             13 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     + 
                     
                       
                         
                           w 
                           
                             31 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             12 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             23 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           w 
                           
                             31 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             13 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           w 
                           
                             32 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             23 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                     - 
                     
                       
                         
                           w 
                           
                             21 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                       ⁢ 
                       
                         
                           w 
                           
                             12 
                             , 
                             0 
                           
                         
                         ⁡ 
                         
                           ( 
                           k 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   38 
                   ) 
                 
               
             
           
         
       
     
     Now a new square matrix v 3 (k) is defined as EQ. (39), and then, EQ. (40) is obtained. 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     39 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             v 
                             3 
                           
                           ⁡ 
                           
                             ( 
                             k 
                             ) 
                           
                         
                         = 
                           
                         ⁢ 
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     v 
                                     11 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     12 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     13 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
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                                     v 
                                     21 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     22 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
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                                     23 
                                   
                                   ⁡ 
                                   
                                     ( 
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                                     ) 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     v 
                                     31 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     32 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                               
                                 
                                   
                                     v 
                                     33 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
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                                     { 
                                     
                                       1 
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                                   / 
                                   
                                     Δ 
                                     3 
                                   
                                 
                               
                               
                                 
                                   
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                                   ⁢ 
                                   
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                                     3 
                                   
                                 
                               
                               
                                 
                                   
                                     { 
                                     
                                       
                                         
                                           
                                             w 
                                             
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                                               , 
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                                             k 
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                                     { 
                                     
                                       1 
                                       - 
                                       
                                         
                                           
                                             w 
                                             
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                                               , 
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                                             ) 
                                           
                                         
                                       
                                     
                                     } 
                                   
                                   / 
                                   
                                     Δ 
                                     3 
                                   
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   39 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     40 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               3 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             
                               
                                 v 
                                 11 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 v 
                                 12 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 v 
                                 13 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 v 
                                 21 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 v 
                                 22 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 v 
                                 23 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                         
                           
                             
                               
                                 v 
                                 31 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 v 
                                 32 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 v 
                                 33 
                               
                               ⁡ 
                               
                                 ( 
                                 k 
                                 ) 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   21 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   31 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   12 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   32 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   3 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   13 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   
                                     u 
                                     ~ 
                                   
                                   23 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   40 
                   ) 
                 
               
             
           
         
       
     
     That is, the current component separating section  650  executes linear combination calculation as given by EQ. 40 in response to the outputs of the subtractors  611 ,  612 ,  613 , and transmits a result thereof to output terminals  604 ,  605 ,  606  as output signals y 1 (k), y 2 (k), y 3 (k). The output signals y 1 (k), y 2 (k), y 3 (k) are also transmitted to delay elements  681 ,  682 ,  683 ,  684 ,  685 ,  686 . 
     The thus-determined first output signal y 1 (k), second output signal y 2 (k), third output signal y 3 (k) are represented by EQs. (30)-(32). That is, under a condition that the following six equations stand, the first output signal y 1 (k) corresponds to the current first signal s 1 (k) generated from the first signal source and mixed with the first mixed signal.
 
 w   21,j ( k )= h   21 ( j )/ h   22 ( j ),  j= 0, 1, 2, . . . ,  N −1
 
 w   12,j ( k )= h   12 ( j )/ h   11 ( j ),  j= 0, 1, 2, . . . ,  N 2−1
 
 w   31,j ( k )= h   31 ( j )/ h   33 ( j ),  j= 0, 1, 2, . . . ,  N 3−1
 
 w   32,j ( k )= h   32 ( j )/ h   33 ( j ),  j= 0, 1, 2, . . . ,  N 4−1
 
 w    13,j ( k )= h   13 ( j )/ h   11 ( j ),  j= 0, 1, 2, . . . ,  N 5−1
 
 w   23,j ( k )= h   23 ( j )/ h   22 ( j ),  j= 0, 1, 2, . . . ,  N 6−1
 
     In this embodiment, coefficients (w 12,0 (k), w 21,0 (k), w 31,0 (k), w 32,0 (k), w 13,0 (k), w 23,0 (k) in the example above) corresponding to the current values of other output signals do not need to be set to zero in the filter. Therefore, signal separation can be achieved for arbitrary coefficients with high accuracy. That is, a desired signal can be extracted with higher accuracy from a mixed signal in which a plurality of signals are mixed. 
     Fourth Embodiment 
       FIG. 8  is a block diagram showing a fourth embodiment of the present invention. A relationship between  FIGS. 7 and 8  corresponds to the relationship between  FIGS. 1 and 4  except that the number of signals to be separated is modified from two to three. As a coefficient updating algorithm, a normalized LMS algorithm or an algorithm as given by EQs. (25) and (26) can be used. Therefore, further details will be omitted. 
     Fifth Embodiment 
     While the preceding description addresses a case in which a mixed signal comprised of two signals is separated in  FIGS. 1 and 4 , and a case in which a mixed signal comprised of three signals is separated in  FIGS. 7 and 8 , a more general case in which a mixed signal comprised of n signals is separated can be similarly considered. In a case that the number of microphones and the number of signal sources are both n, first to n-th output signals y 1 (k), y 2 (k), y 3 (k), . . . , y n (k) are given by the following equation: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     [ 
                     
                       Equation 
                       ⁢ 
                       
                         
                             
                         
                         ⁢ 
                         
                             
                         
                       
                       ⁢ 
                       41 
                     
                     ] 
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             
                               y 
                               1 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           
                             
                               y 
                               2 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             
                               y 
                               n 
                             
                             ⁡ 
                             
                               ( 
                               k 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       
                         [ 
                         
                           
                             
                               1 
                             
                             
                               
                                 
                                   w 
                                   
                                     21 
                                     , 
                                     0 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             
                               … 
                             
                             
                               
                                 
                                   w 
                                   
                                     
                                       n 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                     , 
                                     0 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               
                                 
                                   w 
                                   
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                                   ( 
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                               … 
                             
                             
                               
                                 
                                   w 
                                   
                                     
                                       n 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     , 
                                     0 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                             
                               ⋮ 
                             
                             
                               1 
                             
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 
                                   w 
                                   
                                     
                                       1 
                                       ⁢ 
                                       n 
                                     
                                     , 
                                     0 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             
                               
                                 
                                   w 
                                   
                                     
                                       2 
                                       ⁢ 
                                       n 
                                     
                                     , 
                                     0 
                                   
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                             
                             
                               … 
                             
                             
                               1 
                             
                           
                         
                         ] 
                       
                       
                         - 
                         1 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               
                                 
                                   x 
                                   1 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     
                                       j 
                                       ≠ 
                                       1 
                                     
                                   
                                   n 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     
                                       j 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       1 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   2 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     
                                       j 
                                       = 
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                                       j 
                                       ≠ 
                                       2 
                                     
                                   
                                   n 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     
                                       j 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               
                                 
                                   x 
                                   n 
                                 
                                 ⁡ 
                                 
                                   ( 
                                   k 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     
                                       j 
                                       = 
                                       1 
                                     
                                     
                                       j 
                                       ≠ 
                                       n 
                                     
                                   
                                   n 
                                 
                                 ⁢ 
                                 
                                   
                                     
                                       u 
                                       ~ 
                                     
                                     
                                       j 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       n 
                                     
                                   
                                   ⁡ 
                                   
                                     ( 
                                     k 
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   41 
                   ) 
                 
               
             
           
         
       
     
     An inverse matrix A −1  of an n-th order square matrix A is given by the following equation: 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     42 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     A 
                     
                       - 
                       1 
                     
                   
                   = 
                   
                     
                       1 
                       
                         Δ 
                         n 
                       
                     
                     ⁢ 
                     
                       B 
                       T 
                     
                   
                 
               
               
                 
                   ( 
                   42 
                   ) 
                 
               
             
           
         
       
     
     In this equation, B T  is a transpose of B, which is a cofactor of A. Δ n  is a determinant of A, |A|, and a square matrix B is given by the following equation: 
     
       
         
           
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                       
                           
                       
                       ⁢ 
                       
                           
                       
                     
                     ⁢ 
                     43 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   B 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             b 
                             11 
                           
                         
                         
                           
                             b 
                             21 
                           
                         
                         
                           … 
                         
                         
                           
                             b 
                             
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                           
                         
                       
                       
                         
                           
                             b 
                             12 
                           
                         
                         
                           
                             b 
                             22 
                           
                         
                         
                           … 
                         
                         
                           
                             b 
                             
                               n 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋮ 
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             b 
                             
                               1 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                             
                           
                         
                         
                           
                             b 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               n 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             b 
                             nn 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   43 
                   ) 
                 
               
             
             
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     44 
                   
                   ] 
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     b 
                     ij 
                   
                   = 
                   
                     
                       
                         ( 
                         
                           - 
                           1 
                         
                         ) 
                       
                       
                         p 
                         + 
                         q 
                       
                     
                     ⁢ 
                     
                        
                       
                         
                           b 
                           pq 
                         
                         ⁢ 
                         
                           | 
                           
                             
                               p 
                               ≠ 
                               i 
                             
                             , 
                             
                               q 
                               ≠ 
                               j 
                             
                           
                         
                       
                        
                     
                   
                 
               
               
                 
                   ( 
                   44 
                   ) 
                 
               
             
           
         
       
     
     That is, for an arbitrary number n of signals, a column vector on the right side of EQ. (41) is determined as a first separated signal in which components generated by output signals in the past are separated. By applying thereto the inverse matrix on the right side of EQ. (41) from the left to determine a current output signal, signal separation can be achieved without explicitly using the current output signal. It should be noted that when separating a mixed signal containing n signals, it is necessary to provide n(n−1) filters for separating the past components. 
     Specifically, for a natural number m from one to n, estimated values of first to n-th signals in the past other than an m-th signal in the past are determined, the estimated values are removed from an m-th mixed signal to produce an m-th separated signal, and a signal produced using first to n-th separated signals is output as a first signal. Thus, first to n-th mixed signals in which n signals from the first signal to n-th signal are mixed can be used to extract the first signal. That is, by making a configuration as in the present embodiment, it is possible to separate a desired signal with high accuracy even from a mixed signal in which an arbitrary number of signals are mixed. 
     Another Embodiment 
     According to the first to fifth embodiments in the preceding description, a plurality of mixed signals are wholly processed to separate a signal. However, a process involving dividing a mixed signal into a plurality of sub-band mixed signals, processing the plurality of sub-band mixed signals to determine a plurality of sub-band output signals, and combining the plurality of sub-band output signals to determine an output signal may be contemplated. That is, any one of the embodiments described earlier may be applied after dividing a mixed signal into sub-bands to produce sub-band mixed signals, and a resulting plurality of sub-band output signals may be combined to determine an output signal. By applying sub-band processing, the number of signals can be decreased to reduce the amount of computation. Moreover, since convolution in a time domain (filtering) can be expressed by a simple multiplication, it is possible to reduce the amount of computation. Furthermore, since a sub-band signal spectrum is more planar to be closer to a white signal than a full-band signal spectrum, performance of separation is improved. 
     In such sub-band division processing, time-to-frequency transform such as a band division filter bank, Fourier transform, or cosine transform may be applied. In sub-band synthesis, frequency-to-time transform such as a frequency band synthesis filter bank, inverse Fourier transformation, or inverse cosine transform may be applied. Furthermore, in the time-to-frequency transform and frequency-to-time transform, a window function may be applied to reduce discontinuity at a block border. Consequently, prevention of unusual noises and calculation of accurate sub-band signals become possible. 
     In addition to the embodiments described above, any arbitrary combination thereof is encompassed by the scope of the present invention. Moreover, the present invention may be applied either to a system comprising a plurality of pieces of hardware or a single-unit apparatus. Furthermore, the present invention is applicable to a case in which a signal processing program in software implementing the function of any embodiment is supplied directly or remotely to a system or an apparatus. Therefore, programs installed in a computer, media for storing the programs, and WWW servers allowing download of the programs to implement the function of the present invention in the computer are encompassed by the scope of the present invention. 
       FIG. 9  shows a flow chart illustrating software for implementing the function of the present invention, representing that the flow chart is executed by a computer.  FIG. 9  shows a configuration in which a computer  1000  applies the signal processing described regarding the first to fourth embodiments above in response to mixed signals x 1 (k), x 2 (k) to determine output signals y 1 (k), y 2 (k). Specifically, a first mixed signal and a second mixed signal in which a first signal and a second signal are mixed are first input (S 1001 ). Next, an estimated value of the first signal in the past is determined as a first estimated value, and an estimated value of the second signal in the past is determined as a second estimated value (S 1002 ). Next, the second estimated value is removed from the first mixed signal to produce a first separated signal (S 1003 ). Next, the first estimated value is removed from the second mixed signal to produce a second separated signal (S 1004 ). Furthermore, the first separated signal and second separated signal are used to produce a first output signal (S 1005 ). The first output signal is equal to the original first signal under a certain condition. While the number of input mixed signals is two in  FIG. 9 , this is merely an example and the number may be an arbitrary integer n. 
     While the present invention has been described with reference to embodiments and examples in the preceding description, the present invention is not necessarily limited to the embodiments and examples described above, and several modifications may be made within a scope of the technical idea thereof. 
     The present application claims priority based on Japanese Patent Application No. 2009-229509 filed on Oct. 1, 2009, disclosure of which is incorporated herein as its entirety. 
     REFERENCE SIGNS LIST 
       1 ,  2 ,  601 ,  602 ,  603 , Input terminals (microphones) 
       3 ,  4 ,  611 ,  612 ,  613  Subtractors 
       20 ,  21 ,  620  Past component separating section 
       5 ,  500  Current component separating section 
       6 ,  7 ,  604 ,  605 ,  606  Output terminals 
       8 ,  708  Coefficient adaptation section 
       9 ,  11 ,  103   2 - 103   N1−1 ,  123   2 - 123   N2−1 ,  403 ,  423 ,  681 - 686  Delay elements 
       10 ,  12 ,  631 - 636  Filters 
       51 - 54 ,  102   1 - 102   N1−1 ,  122   1 - 122   N2−1 ,  501 - 504  Multipliers 
       55 ,  56 ,  101   2 - 101   N1−1 ,  121   2 - 121   N2−1  Adders 
       40 ,  42 ,  731 - 736  Adaptive filters 
       1000  Computer