The design of approximate Hilbert transform pairs of wavelet bases

Author

Selesnick, Ivan W.

Author_Institution

Dept. of Electr. & Comput. Eng., Polytech. Univ. Brooklyn, NY, USA

Volume

50

Issue

5

fYear

2002

fDate

5/1/2002 12:00:00 AM

Firstpage

1144

Lastpage

1152

Abstract

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

Keywords

FIR filters; Hilbert transforms; IIR filters; all-pass filters; wavelet transforms; Hilbert transform pair; IIR solutions; allpass filter; biorthogonal FIR solutions; design procedures; dyadic wavelet bases; flat delay response; orthogonal FIR solutions; spectral factorization; vanishing wavelet moments; wavelet-based signal processing; Biomedical signal processing; Delay; Discrete wavelet transforms; Encoding; Finite impulse response filter; IIR filters; Noise reduction; Transient analysis; Wavelet analysis; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.995070

Filename

995070