Wavelet transform with tunable Q-factor

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This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank with real-valued sampling factors. Two forms of the transform are presented. The first form is defined for discrete-time signals defined on all of BBZ. The second form is defined for discrete-time signals of finite-length and can be implemented efficiently with FFTs. The transform is parameterized by its Q-factor and its oversampling rate (redundancy), with modest oversampling rates (e.g., three to four times overcomplete) being sufficient for the analysis/synthesis functions to be well localized.

Original languageEnglish (US)
Article number5752263
Pages (from-to)3560-3575
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - Aug 2011


  • Constant-Q transform
  • Q-factor
  • filter bank
  • wavelet transform

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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