The design of approximate Hilbert transform pairs of wavelet bases

被引：217

作者：

Selesnick, IW ^{[1
]}

机构：

[1] Polytech Univ, Brooklyn, NY 11201 USA

来源：

IEEE TRANSACTIONS ON SIGNAL PROCESSING | 2002年 / 50卷 / 05期

基金：

美国国家科学基金会;

关键词：

dual-tree complex wavelet transform; Hilbert transform; wavelet transforms;

D O I：

10.1109/78.995070

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an approximate Hilbert transform pair. Both orthogonal and biorthogonal FIR solutions are presented, as well as IIR solutions. In each case, the solution depends on an allpass filter having a flat delay response. The design procedure allows for an arbitrary number of vanishing wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results.

引用

页码：1144 / 1152

页数：9

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