Adaptive filtering using filter banks

This paper derives a theory for adaptive filters which operate on filter bank outputs, here called filter bank adaptive filters (FBAFs). It is shown how the FBAFs are a generalization of transform domain adaptive filters and adaptive filters based on structural subband decompositions. The minimum mean-square error performance and convergence properties of FBAFs are determined as a function of filter bank used. A parametrization for a class of FIR perfect reconstruction filter banks is derived which is used to design FBAF's having optimal error performance given prior knowledge of the application. Simulations are performed to illustrate the derived theory and demonstrate the improved error performance of the FBAFs relative to the LMS algorithm, when prior knowledge is incorporated.

[1]  P. P. Vaidyanathan,et al.  Theory and design of M-channel maximally decimated quadrature mirror filters with arbitrary M, having the perfect-reconstruction property , 1987, IEEE Trans. Acoust. Speech Signal Process..

[2]  Karl Pearson F.R.S..  LIII. On lines and planes of closest fit to systems of points in space , 1901 .

[3]  Truong Q. Nguyen,et al.  Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices , 1989, IEEE Trans. Acoust. Speech Signal Process..

[4]  E. Ferrara.  Fast implementations of LMS adaptive filters , 1980 .

[5]  Martin Vetterli,et al.  Adaptive filtering in subbands with critical sampling: analysis, experiments, and application to acoustic echo cancellation , 1992, IEEE Trans. Signal Process..

[6]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[7]  Martin Vetterli,et al.  Perfect reconstruction FIR filter banks: some properties and factorizations , 1989, IEEE Trans. Acoust. Speech Signal Process..

[8]  B. Widrow,et al.  Adaptive filtering in the frequency domain , 1978, Proceedings of the IEEE.

[9]  Sanjit K. Mitra,et al.  STRUCTURAL SUBBAND IMPLEMENTATION OF ADAPTIVE FILTERS , 1990, 1990 Conference Record Twenty-Fourth Asilomar Conference on Signals, Systems and Computers, 1990..

[10]  Gene H. Golub,et al.  Matrix computations , 1983 .

[11]  J. Shynk.  Frequency-domain and multirate adaptive filtering , 1992, IEEE Signal Processing Magazine.

[12]  P. P. Vaidyanathan,et al.  Cosine-modulated FIR filter banks satisfying perfect reconstruction , 1992, IEEE Trans. Signal Process..

[13]  Chong Kwan Un,et al.  A reduced structure of the frequency-domain block LMS adaptive digital filter , 1984 .

[14]  Truong Q. Nguyen,et al.  General synthesis procedures for FIR lossless transfer matrices, for perfect-reconstruction multirate filter bank applications , 1988, IEEE Trans. Acoust. Speech Signal Process..

[15]  W. K. Jenkins,et al.  The use of orthogonal transforms for improving performance of adaptive filters , 1989 .

[16]  A. Peterson,et al.  Transform domain LMS algorithm , 1983 .

[17]  Sanjit K. Mitra,et al.  On The Use Of Filter Banks In Adaptive Filtering , 1988, Twenty-Second Asilomar Conference on Signals, Systems and Computers.

[18]  P. P. Vaidyanathan,et al.  How to capture all FIR perfect reconstruction QMF banks with unimodular matrices? , 1990, IEEE International Symposium on Circuits and Systems.

[19]  D. Luenberger.  Optimization by Vector Space Methods , 1968 .

[20]  M. Vetterli.  Filter banks allowing perfect reconstruction , 1986 .

[21]  Sanjit K. Mitra,et al.  Adaptive line enhancement using multirate techniques , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[22]  C.M. Melas,et al.  Adaptive equalization in magnetic-disk storage channels , 1990, IEEE Communications Magazine.

[23]  A. Gilloire,et al.  Experiments with sub-band acoustic echo cancellers for teleconferencing , 1987, ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[24]  Martin Vetterli,et al.  Adaptive filtering in sub-bands , 1988, ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing.