Hilbert transform pairs of wavelet bases

Ivan W. Selesnick

doi:10.1109/97.923042

Hilbert transform pairs of wavelet bases

Ivan W. Selesnick

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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, that the dual-tree DWT is (nearly) shift-invariant when the scaling filters satisfy the same offset.

Original language	English (US)
Pages (from-to)	170-173
Number of pages	4
Journal	IEEE Signal Processing Letters
Volume	8
Issue number	6
DOIs	https://doi.org/10.1109/97.923042
State	Published - Jun 2001

ASJC Scopus subject areas

Signal Processing
Electrical and Electronic Engineering
Applied Mathematics

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10.1109/97.923042

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title = "Hilbert transform pairs of wavelet bases",

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, that the dual-tree DWT is (nearly) shift-invariant when the scaling filters satisfy the same offset.",

author = "Selesnick, {Ivan W.}",

note = "Funding Information: Manuscript received October 31, 2000. This work was supported by the National Science Foundation CAREER grant CCR-987452. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. A. M. Sayeed. The author is with the Electrical Engineering Department, Polytechnic University, Brooklyn, NY 11201 USA. Publisher Item Identifier S 1070-9908(01)03294-1.",

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Hilbert transform pairs of wavelet bases

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