Overcomplete Discrete Wavelet Transforms With Rational Dilation Factors


Bayram I. , SELESNICK I. W.

IEEE TRANSACTIONS ON SIGNAL PROCESSING, vol.57, no.1, pp.131-145, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 57 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1109/tsp.2008.2007097
  • Title of Journal : IEEE TRANSACTIONS ON SIGNAL PROCESSING
  • Page Numbers: pp.131-145

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.