Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

Ilker Bayram, Ivan W. Selesnick

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

Abstract

Most wavelet transforms used in practice are based on integer sampling factors. Wavelet transforms based on rational sampling factors offer in principle the potential for time-scale signal representations having a finer frequency resolution. Previous work on rational wavelet transforms and filter banks includes filter design methods and frequency domain implementations. We present several specific examples of Daubechies-type filters for a discrete orthonormal rational wavelet transform (FIR filters having a maximum number of vanishing moments) obtained using Gröbner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.

Original languageEnglish (US)
Title of host publicationWavelet Applications in Industrial Processing V
DOIs
StatePublished - 2007
EventWavelet Applications in Industrial Processing V - Boston, MA, United States
Duration: Sep 11 2007Sep 12 2007

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume6763
ISSN (Print)0277-786X

Other

OtherWavelet Applications in Industrial Processing V
CountryUnited States
CityBoston, MA
Period9/11/079/12/07

Keywords

  • Frames
  • Overcomplete filter banks
  • Rational filter banks
  • Rational wavelets

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Bayram, I., & Selesnick, I. W. (2007). Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors. In Wavelet Applications in Industrial Processing V [67630H] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 6763). https://doi.org/10.1117/12.741073