Method and system for on-line blind source separation
A method and apparatus is disclosed for performing blind source separation using convolutive signal decorrelation. For a first embodiment, the method accumulates a length of input signal (mixed signal) that comprises a plurality of independent signals from independent signal sources. The invention then divides the length of input signal into a plurality of T-length periods (windows) and performs a discrete Fourier transform (DFT) on the signal within each T-length period. Thereafter, estimated cross-correlation values are computed using a plurality of the averaged DFT values. A total number of K cross-correlation values are computed, where each of the K values is averaged over N of the T-length periods. Using the cross-correlation values, a gradient descent process computes the coefficients of a FIR filter that will effectively separate the source signals within the input signal. A second embodiment of the invention is directed to on-line processing of the input signal—i.e., processing the signal as soon as it arrives with no storage of the signal data. In particular, an on-line gradient algorithm is provided for application to non-stationary signals and having an adaptive step size in the frequency domain based on second derivatives of the cost function. The on-line separation methodology of this embodiment is characterized as multiple adaptive decorrelation.
1. A method for separating a plurality of mixed signals into a plurality of component signals comprising the steps of:
(a) producing a plurality of discrete Fourier transform (DFT) values corresponding to frequency components of an input segment of said mixed signals;
(b) updating cross correlation estimation matrices using said DFT values;
(c) computing, using a cost-function minimization process, an update value for a plurality of filter coefficients for a finite impulse response (FIR) filter using said cross correlation estimation values;
(d) filtering said mixed signals using said FIR filter having said updated filter coefficients to separate said mixed signals into one or more component signals, wherein at least one of the one or more component signals comprises acoustic waves; and
(e) iteratively repeating steps (a), (b), (c) and (d) for successive input segments of said mixed signal.
2. The method of claim 1 wherein said acoustic waves are created by the body of a living species.
3. The method of claim 1 wherein said acoustic waves are created by industrial processes.
4. The method of claim 1 wherein said acoustic waves are created by chemical processes.
5. The method of claim 1 wherein said acoustic waves are created by equipment, machinery, devices, systems or components.
6. The method of claim 5 wherein said acoustic waves are analog or digital.
7. The method of claim 5 wherein said acoustic waves are created by mechanical, electrical, optical, electro-optical, magnetic or electro-mechanical means.
8. An apparatus for separating a plurality of mixed signals into a plurality of component signals comprising:
means for producing a plurality of discrete Fourier transform (DFT) values corresponding to frequency components of an input segment of said mixed signals;
means for updating cross correlation estimation matrices using said DFT values; a cost-function minimization processor for computing an update value for a plurality of filter coefficients for a finite impulse response (FIR) filter using said cross correlation estimation values; and an FIR filter having said updated filter coefficients to separate said mixed signals into one or more component signals, wherein at least one of the one or more component signals comprises acoustic waves.
9. The apparatus of claim 8 wherein said acoustic waves are created by the body of a living species.
10. The apparatus of claim 8 wherein said acoustic waves are created by industrial processes.
11. The apparatus of claim 8 wherein said acoustic waves are created by chemical processes.
12. The apparatus of claim 8 wherein said acoustic waves are created by analog or digital means.
13. A computer readable storage medium containing a program that, when executed upon a general purpose computer system, causes said general purpose computer system to become a specific purpose computer system that performs a method for separating a plurality of mixed signals into a plurality of component signals comprising the steps of:
(a) producing a plurality of discrete Fourier transform (DFT) values corresponding to frequency components of an input segment of said mixed signals;
(b) updating cross correlation estimation matrices using said DFT values;
(c) computing, using a cost-function minimization process, an update value for a plurality of filter coefficients for a finite impulse response (FIR) filter using said cross correlation estimation values;
(d) filtering said mixed signals using said FIR filter having said updated filter coefficients to separate said mixed signals into one or more component signals, wherein at least one of the one or more component signals comprises acoustic waves; and
(e) iteratively repeating steps (a), (b), (c) and (d) for successive input segments of said mixed signal.
14. The computer readable storage medium of claim 13 wherein said acoustic waves are created by the body of a living species.
15. The computer readable storage medium of claim 13 wherein said acoustic waves are created by industrial processes.
16. The computer readable storage medium of claim 13 wherein said acoustic waves are created by chemical processes.
17. The computer readable storage medium of claim 13 wherein said acoustic waves are created by mechanical processes.
18. The computer readable storage medium of claim 13 wherein said acoustic waves are created by electrical processes.
19. The computer readable storage medium of claim 13 wherein said acoustic waves are created by optical processes.