Complex wavelet transforms with allpass filters

Felix C.A. Fernandes, Ivan W. Selesnick, Rutger L.C. Van Spaendonck, C. Sidney Burrus

Research output: Contribution to journalArticlepeer-review


Complex discrete wavelet transforms (DWT) have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex DWT.

Original languageEnglish (US)
Pages (from-to)1689-1706
Number of pages18
JournalSignal Processing
Issue number8
StatePublished - Aug 2003


  • Complex wavelets
  • Dual-tree
  • Fractional delay
  • Minimax allpass filters
  • Non-redundant Hilbert transform

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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