Symmetric wavelet tight frames with two generators

Ivan Selesnick, A. Farras Abdelnour

Research output: Contribution to journalArticle

Abstract

This paper uses the UEP approach for the construction of wavelet tight frames with two (anti-) symmetric wavelets, and provides some results and examples that complement recent results by Q. Jiang. A description of a family of solutions when the lowpass scaling filter is of even-length is provided. When one wavelet is symmetric and the other is antisymmetric, the wavelet filters can be obtained by a simple procedure based on matching the roots of associated polynomials. The design examples in this paper begin with the construction of a lowpass filter h0(n) that is designed so as to ensure that both wavelets have at least a specified number of vanishing moments.

Original languageEnglish (US)
Pages (from-to)211-225
Number of pages15
JournalApplied and Computational Harmonic Analysis
Volume17
Issue number2 SPEC. ISS.
DOIs
StatePublished - Sep 2004

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Wavelet Frames
Tight Frame
Wavelets
Generator
Antisymmetric
Polynomials
Filter
Vanishing Moments
Associated Polynomials
Low-pass Filter
Complement
Roots
Scaling

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Symmetric wavelet tight frames with two generators. / Selesnick, Ivan; Abdelnour, A. Farras.

In: Applied and Computational Harmonic Analysis, Vol. 17, No. 2 SPEC. ISS., 09.2004, p. 211-225.

Research output: Contribution to journalArticle

Selesnick, Ivan ; Abdelnour, A. Farras. / Symmetric wavelet tight frames with two generators. In: Applied and Computational Harmonic Analysis. 2004 ; Vol. 17, No. 2 SPEC. ISS. pp. 211-225.
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