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 s1(k) from a desired signal source 910 can be assumed to be convolved with an impulse response h11 (a transfer function H11) of an acoustic space from the desired signal source 910 to a microphone 901 before the signal s1(k) reaches the microphone 901. On the other hand, a noise s2(k) from the noise source 920 can also be assumed to be convolved with an impulse response h21 (a transfer function H21) of an acoustic space from the noise source 920 to the microphone 901 before the noise s2(k) reaches the microphone 901. Therefore, a voice signal x1(k) output from the microphone 901 at a time k is a mixed signal expressed by EQ. (1) below.
Similarly, the desired signal s1(k) from the desired signal source 910 can be assumed to be convolved with an impulse response h12 (a transfer function H12) of an acoustic space from the desired signal source 910 to a microphone 902 before the signal s1(k) reaches the microphone 902. On the other hand, the noise s2(k) from the noise source 920 can also be assumed to be convolved with an impulse response h22 (a transfer function H22) of an acoustic space from the noise source 920 to the microphone 902 before the noise s2(k) reaches the microphone 902. Therefore, a voice signal x2(k) output from the microphone 902 at the time k is a mixed signal expressed by EQ. (2) below.
                    [                  Equation          ⁢                                          ⁢          1                ]                                                                                  x            1                    ⁡                      (            k            )                          =                                            ∑                              j                =                0                                                              M                  ⁢                                                                          ⁢                  1                                -                1                                      ⁢                                                            h                  11                                ⁡                                  (                  j                  )                                            ⁢                                                s                  1                                ⁡                                  (                                      k                    -                    j                                    )                                                              +                                    ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  1                                -                1                                      ⁢                                                            h                  21                                ⁡                                  (                  j                  )                                            ⁢                                                s                  2                                ⁡                                  (                                      k                    -                    j                                    )                                                                                        (        1        )                                [                  Equation          ⁢                                          ⁢          2                ]                                                                                  x            2                    ⁡                      (            k            )                          =                                            ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  2                                -                1                                      ⁢                                                            h                  12                                ⁡                                  (                  j                  )                                            ⁢                                                s                  1                                ⁡                                  (                                      k                    -                    j                                    )                                                              +                                    ∑                              j                =                0                                                              M                  ⁢                                                                          ⁢                  2                                -                1                                      ⁢                                                            h                  22                                ⁡                                  (                  j                  )                                            ⁢                                                s                  2                                ⁡                                  (                                      k                    -                    j                                    )                                                                                        (        2        )            
In these equations, h11(j), h12(j), h21(j), h22(j) correspond to the transfer functions H11, H12, H21, H22 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 H11, H12, H21, H22 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 h11(0)=1, so that EQ. (1) can be rewritten into EQ. (3) below.
                    [                  Equation          ⁢                                          ⁢          3                ]                                                                                  x            1                    ⁡                      (            k            )                          =                                            s              1                        ⁡                          (              k              )                                +                                    ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  1                                -                1                                      ⁢                                                            h                  21                                ⁡                                  (                  j                  )                                            ⁢                                                s                  2                                ⁡                                  (                                      k                    -                    j                                    )                                                                                        (        3        )            
Similarly, when the microphone 902 lies sufficiently close to the noise source 920, M2−1=0 and h22(0)=1, so that EQ. (2) can be rewritten into EQ. (4) below.
                    [                  Equation          ⁢                                          ⁢          4                ]                                                                                  x            2                    ⁡                      (            k            )                          =                                            ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  2                                -                1                                      ⁢                                                            h                  12                                ⁡                                  (                  j                  )                                            ⁢                                                s                  1                                ⁡                                  (                                      k                    -                    j                                    )                                                              +                                    s              2                        ⁡                          (              k              )                                                          (        4        )            
At that time, an output y1(k) of a subtractor 903 is a signal obtained by subtracting an output u1(k) of an adaptive filter 907 from the signal x1(k) of the microphone 901, as expressed by EQ. (5) below. On the other hand, y2(k) is signal obtained by subtracting an output u2(k) of an adaptive filter 908 from the signal x2(k) of the microphone 902, as expressed by EQ. (6) below. In these equations, w21,j(k), w12,j(k) are coefficients of the adaptive filters 907, 908.
                    [                  Equation          ⁢                                          ⁢          5                ]                                                                                  y            1                    ⁢                                          ⁢                      (            k            )                          =                                                            x                1                            ⁡                              (                k                )                                      -                                          u                1                            ⁡                              (                k                )                                              =                                                    x                1                            ⁡                              (                k                )                                      -                                          ∑                                  j                  =                  0                                                                      N                    ⁢                                                                                  ⁢                    1                                    -                  1                                            ⁢                                                                    w                                          21                      ,                      j                                                        ⁡                                      (                    k                    )                                                  ⁢                                                      y                    2                                    ⁡                                      (                                          k                      -                      j                                        )                                                                                                          (        5        )                                [                  Equation          ⁢                                          ⁢          6                ]                                                                                  y            2                    ⁡                      (            k            )                          =                                                            x                2                            ⁡                              (                k                )                                      -                                          u                2                            ⁡                              (                k                )                                              =                                                    x                2                            ⁡                              (                k                )                                      -                                          ∑                                  j                  =                  0                                                                      N                    ⁢                                                                                  ⁢                    2                                    -                  1                                            ⁢                                                                    w                                          12                      ,                      j                                                        ⁡                                      (                    k                    )                                                  ⁢                                                      y                    1                                    ⁡                                      (                                          k                      -                      j                                        )                                                                                                          (        6        )            
That is, the output u1(k) of the adaptive filter 907 is a pseudo noise, and the output u2(k) of the adaptive filter 908 is a pseudo crosstalk. Ultimately, y1(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 y1(k) is given by the following equation.
                    [                  Equation          ⁢                                          ⁢          7                ]                                                                                  y            1                    ⁡                      (            k            )                          =                                            s              1                        ⁡                          (              k              )                                +                                    ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  1                                -                1                                      ⁢                                                            h                  21                                ⁡                                  (                  j                  )                                            ⁢                                                s                  2                                ⁡                                  (                                      k                    -                    j                                    )                                                              -                                    ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  1                                -                1                                      ⁢                                                            w                                      21                    ,                                                  ⁡                                  (                  k                  )                                            ⁢                                                y                  2                                ⁡                                  (                                      k                    -                    j                                    )                                                                                        (        7        )            
That is, y1(k)=s1(k) stands when y2(k)=s2(k) and w21,j(k)=h21(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 y2(k) of the subtractor 904 is output as one of the extracted signals. Moreover, coefficients for adaptive filters 917, 918 are updated using y1(k) and y2(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 y2(k).
                    [                  Equation          ⁢                                          ⁢          8                ]                                                                                  y            2                    ⁡                      (            k            )                          =                                            s              2                        ⁡                          (              k              )                                +                                    ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  2                                -                1                                      ⁢                                                            h                  12                                ⁡                                  (                  j                  )                                            ⁢                                                s                  1                                ⁡                                  (                                      k                    -                    j                                    )                                                              -                                    ∑                              j                =                0                                                              N                  ⁢                                                                          ⁢                  2                                -                1                                      ⁢                                                            w                                      12                    ,                    j                                                  ⁡                                  (                  k                  )                                            ⁢                                                y                  1                                ⁡                                  (                                      k                    -                    j                                    )                                                                                        (        8        )            
Since perfect signal separation is achieved only when y1(k)=s1(k) and y2(k)=s2(k) stand, the following two equations should stand as a requirement therefor.w21,j(k)=h21(j), j=0, 1, 2, . . . , N1−1w12,j(k)=h12(j), j=0, 1, 2, . . . , N2−1
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.w21,j(k)=h21(j)/h22(j), j=0, 1, 2, . . . , N1−1w12,j(k)=h12(j)/h11(j), j=0, 1, 2, . . . , N2−1