FIR paraunitary filter banks given several analysis filters: factorizations and constructions

FIR paraunitary filter banks have been extensively studied and well understood. We address the following problem: how to characterize and construct an FIR paraunitary filter bank when its several analysis filters are given a priori. To study this problem is not only useful in orthogonal M-band wavelets with certain regularity where we need to construct wavelet filters when a scaling filter with certain regularity is found a priori but is also useful in the design of multirate filter banks where we have already had several desired analysis filters. One such example is multiwavelet transforms. We present a method of constructing all possible FIR paraunitary filter banks in terms of a McMillan degree when several analysis filters are given.

[1]  Xiang-Gen Xia,et al.  Vector-valued wavelets and vector filter banks , 1996, IEEE Trans. Signal Process..

[2]  George C. Donovan,et al.  Construction of Orthogonal Wavelets Using Fractal Interpolation Functions , 1996 .

[3]  Gilbert Strang,et al.  Short wavelets and matrix dilation equations , 1995, IEEE Trans. Signal Process..

[4]  Ahmed H. Tewfik,et al.  Discrete orthogonal M-band wavelet decompositions , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

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

[6]  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..

[7]  M. Vetterli,et al.  Time-varying filter banks and multiwavelets , 1994, Proceedings of IEEE 6th Digital Signal Processing Workshop.

[8]  Xiang-Gen Xia,et al.  Design of prefilters for discrete multiwavelet transforms , 1996, IEEE Trans. Signal Process..

[9]  Peter N. Heller,et al.  Theory of regular M-band wavelet bases , 1993, IEEE Trans. Signal Process..

[10]  P. Vaidyanathan Multirate Systems And Filter Banks , 1992 .

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

[12]  D. Hardin,et al.  Fractal Functions and Wavelet Expansions Based on Several Scaling Functions , 1994 .

[13]  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..

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

[15]  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..