The design of approximate Hilbert transform pairs of wavelet bases

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Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. In each case, the solution depends on an allpass filter having a flat delay response. The design procedure allows for an arbitrary number of vanishing wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results.

Original languageEnglish (US)
Pages (from-to)1144-1152
Number of pages9
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - May 2002


  • Dual-tree complex wavelet transform
  • Hilbert transform
  • Wavelet transforms

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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