Optimization of symmetric self-hilbertian filters for the dual-tree complex wavelet transform

Bogdan Dumitrescu, Ilker Bayram, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


In this letter, we expand upon the method of Tay for the design of orthonormal ldquoQ-shiftrdquo filters for the dual-tree complex wavelet transform. The method of Tay searches for good Hilbert-pairs in a one-parameter family of conjugate-quadrature filters that have one vanishing moment less than the Daubechies conjugate-quadrature filters (CQFs). In this letter, we compute feasible sets for one- and two-parameter families of CQFs by employing the trace parameterization of nonnegative trigonometric polynomials and semidefinite programming. This permits the design of CQF pairs that define complex wavelets that are more nearly analytic, yet still have a high number of vanishing moments.

Original languageEnglish (US)
Pages (from-to)146-149
Number of pages4
JournalIEEE Signal Processing Letters
StatePublished - 2008


  • Complex wavelet
  • Hilbert pair
  • Orthogonal filter banks
  • Positive trigonometric polynomials

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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