A new design algorithm for two-band orthonormal rational filter banks and orthonormal rational wavelets

We present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (e,g., regularity). Although the filters obtained from this algorithm are suboptimally designed, they show excellent frequency selectivity. After an in-depth account of the algorithm, we discuss the properties of the rational wavelets generated by some designed filters. In particular, we stress the possibility to design "almost" shift error-free wavelets, which allows the implementation of a rational wavelet transform.

[1]  Truong Q. Nguyen,et al.  Two-channel perfect-reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters , 1989, IEEE Trans. Acoust. Speech Signal Process..

[2]  Thomas P. Barnwell,et al.  The design of perfect reconstruction nonuniform band filter banks , 1991, [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing.

[3]  I. Daubechies,et al.  Othonormal bases of compactly supported wavelets III: better frequency resolution , 1993 .

[4]  John Princen.  The design of nonuniform modulated filterbanks , 1995, IEEE Trans. Signal Process..

[5]  Thierry BLUzAbstract.  SIMPLE REGULARITY CRITERIA FOR SUBDIVISION SCHEMES , 1997 .

[6]  P. P. Vaidyanathan,et al.  Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial , 1990, Proc. IEEE.

[7]  O. Rioul,et al.  A Remez exchange algorithm for orthonormal wavelets , 1994 .

[8]  S. Wada.  Design of nonuniform division multirate FIR filter banks , 1995 .

[9]  Olivier Rioul.  On the choice of 'wavelet' filter for still image compression , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[10]  Fred Mintzer,et al.  Filters for distortion-free two-band multirate filter banks , 1985, IEEE Trans. Acoust. Speech Signal Process..

[11]  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..

[12]  I. Daubechies,et al.  Two-scale difference equations I: existence and global regularity of solutions , 1991 .

[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]  Jelena Kovacevic,et al.  Perfect reconstruction filter banks with rational sampling factors , 1993, IEEE Trans. Signal Process..

[15]  Thierry Blu.  Lossless filter design in two-band rational filter banks : A new algorithm , 1993 .

[16]  Truong Q. Nguyen,et al.  Structures for M-channel perfect-reconstruction FIR QMF banks which yield linear-phase analysis filters , 1990, IEEE Trans. Acoust. Speech Signal Process..

[17]  Olivier Rioul.  Ondelettes regulieres. Application a la compression d'images fixes , 1993 .

[18]  Thierry Blu,et al.  An iterated rational filter bank for audio coding , 1996, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96).

[19]  G. MallatS..  A Theory for Multiresolution Signal Decomposition , 1989 .

[20]  P. P. Vaidyanathan,et al.  Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks , 1988, IEEE Trans. Acoust. Speech Signal Process..

[21]  Thierry Blu.  Shift error in iterated rational filter banks , 1996, 1996 8th European Signal Processing Conference (EUSIPCO 1996).

[22]  L.R. Rabiner,et al.  Interpolation and decimation of digital signals—A tutorial review , 1981, Proceedings of the IEEE.

[23]  Mark J. T. Smith,et al.  Time-domain filter bank analysis: a new design theory , 1992, IEEE Trans. Signal Process..

[24]  Martin Vetterli,et al.  Oversampled filter banks , 1998, IEEE Trans. Signal Process..

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

[26]  Mark J. T. Smith,et al.  Exact reconstruction techniques for tree-structured subband coders , 1986, IEEE Trans. Acoust. Speech Signal Process..

[27]  Martin Vetterli,et al.  A theory of multirate filter banks , 1987, IEEE Trans. Acoust. Speech Signal Process..

[28]  P. Vaidyanathan,et al.  Non-uniform multirate filter banks: theory and design , 1989, IEEE International Symposium on Circuits and Systems,.

[29]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Jelena Kovacevic,et al.  Filter banks and wavelets: Extensions and applications , 1992, Signal Processing.

[31]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[32]  James D. Johnston,et al.  A filter family designed for use in quadrature mirror filter banks , 1980, ICASSP.

[33]  Thierry Blu.  Iterated filter banks with rational rate changes connection with discrete wavelet transforms , 1993, IEEE Trans. Signal Process..