Balanced multiwavelet bases based on symmetric FIR filters

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 φi,j. This paper also introduces new K-balanced orthogonal multiwavelet bases based on symmetric FIR filters. The nonlinear design equations arising in this work are solved using Grobner 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.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
PublisherSociety of Photo-Optical Instrumentation Engineers
Pages122-131
Number of pages10
Volume3813
StatePublished - 1999
EventProceedings of the 1999 Wavelet Applications in Signal and Image Processing VII - Denver, CO, USA
Duration: Jul 19 1999Jul 23 1999

Other

OtherProceedings of the 1999 Wavelet Applications in Signal and Image Processing VII
CityDenver, CO, USA
Period7/19/997/23/99

Fingerprint

FIR filters
Filter banks
scalars
moments
filters
scaling

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Selesnick, I. (1999). Balanced multiwavelet bases based on symmetric FIR filters. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 3813, pp. 122-131). Society of Photo-Optical Instrumentation Engineers.

Balanced multiwavelet bases based on symmetric FIR filters. / Selesnick, Ivan.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3813 Society of Photo-Optical Instrumentation Engineers, 1999. p. 122-131.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Selesnick, I 1999, Balanced multiwavelet bases based on symmetric FIR filters. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 3813, Society of Photo-Optical Instrumentation Engineers, pp. 122-131, Proceedings of the 1999 Wavelet Applications in Signal and Image Processing VII, Denver, CO, USA, 7/19/99.
Selesnick I. Balanced multiwavelet bases based on symmetric FIR filters. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3813. Society of Photo-Optical Instrumentation Engineers. 1999. p. 122-131
Selesnick, Ivan. / Balanced multiwavelet bases based on symmetric FIR filters. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 3813 Society of Photo-Optical Instrumentation Engineers, 1999. pp. 122-131
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