Overcomplete discrete wavelet transforms with rational dilation factors

Iiker Bayram, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - 2009


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

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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