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

Dumitrescu B., Bayram I., Selesnick I. W.

IEEE SIGNAL PROCESSING LETTERS, vol.15, pp.146-149, 2008 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15
  • Publication Date: 2008
  • Doi Number: 10.1109/lsp.2007.913609
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.146-149
  • Istanbul Technical University Affiliated: No


In this letter, we expand upon the method of Tay et al for the design of orthonormal "Q-shift" filters for the dual-tree complex wavelet transform. The method of Tay et al 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.