Overcomplete discrete wavelet transforms with rational dilation factors

Iiker Bayram, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

This paper develops an overcomplete discrete wavelet transform (DWT) based on rational dilation factors for discrete-time signals. The proposed overcomplete rational DWT is implemented using self-inverting FIR filter banks, is approximately shift-invariant, and can provide a dense sampling of the time-frequency plane. A straightforward algorithm is described for the construction of minimal-length perfect reconstruction filters with a specified number of vanishing moments; whereas, in the nonredundant rational case, no such algorithm is available. The algorithm is based on matrix spectral factorization. The analysis/synthesis functions (discrete-time wavelets) can be very smooth and can be designed to closely approximate the derivatives of the Gaussian function.

Original languageEnglish (US)
Pages (from-to)131-145
Number of pages15
JournalIEEE Transactions on Signal Processing
Volume57
Issue number1
DOIs
StatePublished - 2009

Fingerprint

Discrete wavelet transforms
Filter banks
FIR filters
Factorization
Sampling
Derivatives

Keywords

  • Filter bank
  • Frame
  • Matrix spectral factorization
  • Rational dilation factor
  • Wavelet transforms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing

Cite this

Overcomplete discrete wavelet transforms with rational dilation factors. / Bayram, Iiker; Selesnick, Ivan.

In: IEEE Transactions on Signal Processing, Vol. 57, No. 1, 2009, p. 131-145.

Research output: Contribution to journalArticle

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