A generalized parametric PR-QMF design technique based on Bernstein polynomial approximation

A generalized, parametric, perfect-reconstruction quadrature-mirror-filter (PR-QMF) design technique based on Bernstein polynomial approximation in the magnitude-square domain is presented. The parametric nature of this solution provides useful insights to the PR-QMF problem. Several well-known orthonormal wavelet filters, PR-QMFs, are shown to be the special cases of the proposed technique. Energy compaction performances of a few popular signal decomposition techniques are presented for AR(1) signal sources. It is observed that the hierarchical QMF filter banks considered outperform the block transforms as expected. >

[1]  Philippe Michel Cassereau.  A new class of optimal unitary transforms for image processing , 1985 .

[2]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[3]  Hamid Gharavi,et al.  Sub-Band Coding Of Digital Images Using Two-Dimensional Quadrature Mirror Filtering , 1986, Other Conferences.

[4]  O. Herrmann.  On the approximation problem in nonrecursive digital filter design , 1971 .

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

[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]  S. D. Roy,et al.  Design of maximally-flat FIR filters using the Bernstein polynomial , 1987 .

[8]  James L. Flanagan,et al.  Digital coding of speech in sub-bands , 1976, The Bell System Technical Journal.

[9]  D. Esteban,et al.  Application of quadrature mirror filters to split band voice coding schemes , 1977 .

[10]  I. Daubechies.  Orthonormal bases of compactly supported wavelets II: variations on a theme , 1993 .

[11]  Michel Barlaud,et al.  Image coding using vector quantization in the wavelet transform domain , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[12]  P. Vaidyanathan.  Quadrature mirror filter banks, M-band extensions and perfect-reconstruction techniques , 1987, IEEE ASSP Magazine.

[13]  M. Vetterli.  Multi-dimensional sub-band coding: Some theory and algorithms , 1984 .

[14]  John W. Woods,et al.  Subband coding of images , 1986, IEEE Trans. Acoust. Speech Signal Process..

[15]  J. A. Miller.  Maximally flat nonrecursive digital filters , 1972 .

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

[17]  A.N. Akansu,et al.  The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition , 1993, IEEE Trans. Signal Process..

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

[19]  Henrique S. Malvar,et al.  The LOT: transform coding without blocking effects , 1989, IEEE Trans. Acoust. Speech Signal Process..