The design of Hilbert transform pairs of wavelet bases via the flat delay filter

Author

Selesnick, Ivan W.

Author_Institution

Polytech. Univ., Brooklyn, NY, USA

Volume

6

fYear

2001

fDate

2001

Firstpage

3673

Abstract

This paper describes a simple procedure, based on spectral factorization, for the design of a pair of orthonormal wavelet bases where the two wavelets form a Hilbert transform pair. The two scaling filters respectively have the numerator and denominator of the flat delay all-pass filter as factors. The design procedure allows for an arbitrary number of zero wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results

Keywords

Hilbert transforms; all-pass filters; delay filters; signal resolution; spectral analysis; wavelet transforms; Hilbert transform pairs; Matlab program; all-pass filter; flat delay filter; orthonormal wavelet bases; scaling filters; spectral factorization; wavelet bases; zero wavelet moments; Algorithm design and analysis; Discrete wavelet transforms; Encoding; Finite impulse response filter; Fourier transforms; IIR filters; Noise reduction; Nonlinear equations; Propagation delay; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 2001. Proceedings. (ICASSP '01). 2001 IEEE International Conference on

Conference_Location

Salt Lake City, UT

ISSN

1520-6149

Print_ISBN

0-7803-7041-4

Type

conf

DOI

10.1109/ICASSP.2001.940639

Filename

940639