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

Ilker Bayram, Ivan 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
Volume6763
DOIs
StatePublished - 2007
EventWavelet Applications in Industrial Processing V - Boston, MA, United States
Duration: Sep 11 2007Sep 12 2007

Other

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

Fingerprint

wavelet analysis
Wavelet transforms
sampling
Sampling
FIR filters
filters
Filter banks
Factorization
factorization
integers
polynomials
Polynomials
moments
matrices

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors. / Bayram, Ilker; Selesnick, Ivan.

Wavelet Applications in Industrial Processing V. Vol. 6763 2007. 67630H.

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

Bayram, I & Selesnick, I 2007, Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors. in Wavelet Applications in Industrial Processing V. vol. 6763, 67630H, Wavelet Applications in Industrial Processing V, Boston, MA, United States, 9/11/07. https://doi.org/10.1117/12.741073
Bayram, Ilker ; Selesnick, Ivan. / Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors. Wavelet Applications in Industrial Processing V. Vol. 6763 2007.
@inproceedings{6a1b5a9edc354bbb8841da6c23cb3e9b,
title = "Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors",
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 Gr{\"o}bner bases. We also present the design of overcomplete rational wavelet transforms (tight frames) with FIR filters obtained using polynomial matrix spectral factorization.",
keywords = "Frames, Overcomplete filter banks, Rational filter banks, Rational wavelets",
author = "Ilker Bayram and Ivan Selesnick",
year = "2007",
doi = "10.1117/12.741073",
language = "English (US)",
isbn = "9780819469236",
volume = "6763",
booktitle = "Wavelet Applications in Industrial Processing V",

}

TY - GEN

T1 - Design of orthonormal and overcomplete wavelet transforms based on rational sampling factors

AU - Bayram, Ilker

AU - Selesnick, Ivan

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Frames

KW - Overcomplete filter banks

KW - Rational filter banks

KW - Rational wavelets

UR - http://www.scopus.com/inward/record.url?scp=42449132214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42449132214&partnerID=8YFLogxK

U2 - 10.1117/12.741073

DO - 10.1117/12.741073

M3 - Conference contribution

AN - SCOPUS:42449132214

SN - 9780819469236

VL - 6763

BT - Wavelet Applications in Industrial Processing V

ER -