Research PaperNo Access

Optimization in the construction of cardinal and symmetric wavelets on the line

Neil D. Dizon

School of Information and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia

E-mail Address: neilkristofer.dizon@uon.edu.au

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Jeffrey A. Hogan

School of Information and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia

E-mail Address: jeff.hogan@newcastle.edu.au

Corresponding author.

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, and

Joseph D. Lakey

Department of Mathematics Sciences, New Mexico State University, Las Cruces, NM 88003-8001, USA

E-mail Address: jlakey@nmsu.edu

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https://doi.org/10.1142/S021969132150048XCited by:0 (Source: Crossref)

Abstract

We present an optimization approach to wavelet architecture that hinges on the Zak transform to formulate the construction as a minimization problem. The transform warrants parametrization of the quadrature mirror filter in terms of the possible integer sample values of the scaling function and the associated wavelet. The parameters are predicated to satisfy constraints derived from the conditions of regularity, compact support and orthonormality. This approach allows for the construction of nearly cardinal scaling functions when an objective function that measures deviation from cardinality is minimized. A similar objective function based on a measure of symmetry is also proposed to facilitate the construction of nearly symmetric scaling functions on the line.

Keywords:

AMSC: 42C40, 42B99, 65T60, 47N10

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