Frequency-domain design of overcomplete rational-dilation wavelet transforms

IIlker Bayram, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


The dyadic wavelet transform is an effective tool for processing piecewise smooth signals; however, its poor frequency resolution (its low Q-factor) limits its effectiveness for processing oscillatory signals like speech, EEG, and vibration measurements, etc. This paper develops a more flexible family of wavelet transforms for which the frequency resolution can be varied. The new wavelet transform can attain higher Q-factors (desirable for processing oscillatory signals) or the same low Q-factor of the dyadic wavelet transform. The new wavelet transform is modestly overcomplete and based on rational dilations. Like the dyadic wavelet transform, it is an easily invertible 'constant-Q' discrete transform implemented using iterated filter banks and can likewise be associated with a wavelet frame for L2 (ℝ). The wavelet can be made to resemble a Gabor function and can hence have good concentration in the time-frequency plane. The construction of the new wavelet transform depends on the judicious use of both the transform's redundancy and the flexibility allowed by frequency-domain filter design.

Original languageEnglish (US)
Pages (from-to)2957-2972
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number8
StatePublished - 2009


  • Constant-Q transform
  • Multirate filter banks
  • Q factor
  • Rational-dilation wavelet transform
  • Wavelet transforms

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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