Balanced multiwavelet bases based on symmetric FIR filters

Ivan W. Selesnick

doi:10.1117/12.366773

26 October 1999 Balanced multiwavelet bases based on symmetric FIR filters

Ivan W. Selesnick

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366773
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

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.

Citation Download Citation

Ivan W. Selesnick "Balanced multiwavelet bases based on symmetric FIR filters", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366773

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