Symmetric wavelet tight frames with two generators

Ivan W. Selesnick; A. Farras Abdelnour

doi:10.1016/j.acha.2004.05.003

Symmetric wavelet tight frames with two generators

Ivan W. Selesnick, A. Farras Abdelnour

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	211-225
Number of pages	15
Journal	Applied and Computational Harmonic Analysis
Volume	17
Issue number	2 SPEC. ISS.
DOIs	https://doi.org/10.1016/j.acha.2004.05.003
State	Published - Sep 2004

ASJC Scopus subject areas

Applied Mathematics

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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.",

author = "Selesnick, {Ivan W.} and Abdelnour, {A. Farras}",

note = "Funding Information: ✩ Research supported by ONR Grant N00014-03-1-0217. * Corresponding author. E-mail addresses: selesi@poly.edu (I.W. Selesnick), farras@taco.poly.edu (A.F. Abdelnour).",

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AU - Abdelnour, A. Farras

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Symmetric wavelet tight frames with two generators

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