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Proceedings Paper

Balanced multiwavelet bases based on symmetric FIR filters
Author(s): Ivan W. Selesnick
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Paper Abstract

This paper describes a basic difference between multiwavelets and scalar wavelets that explains, without using zero moment properties, why certain complications arise in the implementation of discrete multiwavelet transforms. Assuming one wishes to avoid the use of prefilters in implementing the discrete multiwavelet transform, it is suggested that the behavior of the iterated filter bank associated with a multiwavelet basis of multiplicity r is more fully revealed by an expanded set of r2 scaling functions (phi) i,j. This paper also introduces new K-balanced orthogonal multiwavelet bases based on symmetric FIR filers. The nonlinear design equations arising in this work are solved using Groebner bases. The K-balanced multiwavelet bases based on even- length symmetric FIR filters are shown to be particularly well behaved, as illustrated by special relations they satisfy and by the examples constructed.

Paper Details

Date Published: 26 October 1999
PDF: 10 pages
Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); doi: 10.1117/12.366773
Show Author Affiliations
Ivan W. Selesnick, Polytechnic Univ. (United States)

Published in SPIE Proceedings Vol. 3813:
Wavelet Applications in Signal and Image Processing VII
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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