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Conjugate Symmetric Complex Tight Wavelet Frames with Two Generators

Published online by Cambridge University Press:  28 May 2015

Yanmei Xue ,
Ning Bi  and
Yuan Zhang
Yanmei Xue*
Affiliation:
School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R. China
Ning Bi*
Affiliation:
Guangdong Province Key Laboratory of Computational Science, School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, P.R. China
Yuan Zhang*
Affiliation:
School of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing 210044, P.R. China
*
Corresponding author.Email address:ymxuel@163.com
Corresponding author.Email address:mcsbn@mail.sysu.edu.cn
Corresponding author.Email address:zhangyuanmath@yahoo.com.en
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Abstract

Two algorithms for constructing a class of compactly supported conjugate symmetric complex tight wavelet frames ψ = {ψ1, ψ2} are derived. Firstly, a necessary and sufficient condition for constructing the conjugate symmetric complex tight wavelet frames is established. Secondly, based on a given conjugate symmetric low pass filter, a description of a family of complex wavelet frame solutions is provided when the low pass filter is of even length. When one wavelet is conjugate symmetric and the other is conjugate antisymmetric, the two wavelet filters can be obtained by matching the roots of associated polynomials. Finally, two examples are given to illustrate how to use our method to construct conjugate symmetric complex tight wavelet frames which have some vanishing moments.

Keywords

42C1594A12Complex tight wavelet frameconjugate symmetry vanishing moments
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 6 , Issue 2 , May 2013 , pp. 353 - 363
Copyright
Copyright © Global Science Press Limited 2013

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