DocumentCode
1488873
Title
Hilbert transform pairs of wavelet bases
Author
Selesnick, Ivan W.
Author_Institution
Dept. of Electr. Eng., Polytech. Univ., Brooklyn, NY, USA
Volume
8
Issue
6
fYear
2001
fDate
6/1/2001 12:00:00 AM
Firstpage
170
Lastpage
173
Abstract
This paper considers the design of pairs of wavelet bases where the wavelets form a Hilbert transform pair. The derivation is based on the limit functions defined by the infinite product formula. It is found that the scaling filters should be offset from one another by a half sample. This gives an alternative derivation and explanation for the result by Kingsbury (1999), that the dual-tree DWT is (nearly) shift-invariant when the scaling filters satisfy the same offset.
Keywords
Hilbert transforms; filtering theory; signal processing; wavelet transforms; Hilbert transform pairs; dual-tree DWT; half sample; infinite product formula; limit functions; scaling filters; shift-invariant; signal processing; wavelet bases; Delay; Discrete transforms; Discrete wavelet transforms; Encoding; Filter bank; Fourier transforms; Signal processing; Transient analysis; Wavelet analysis; Wavelet transforms;
fLanguage
English
Journal_Title
Signal Processing Letters, IEEE
Publisher
ieee
ISSN
1070-9908
Type
jour
DOI
10.1109/97.923042
Filename
923042
Link To Document