Title :
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
fDate :
5/1/2002 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
