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   -> Volume 6, Issue 3

Preprint: Orthogonal Complex Filter Banks and Wavelets
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"Xiao-Ping ZHANG" (

PostPosted: Tue Feb 25, 1997 10:30 pm    
Subject: Preprint: Orthogonal Complex Filter Banks and Wavelets
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#6 Preprint: Orthogonal Complex Filter Banks and Wavelets

Dear Sir,

I would like to make the following preprint available to wavelet digest

Title: Orthogonal Complex Filter Banks and Wavelets: Some Properties
and Design

Authors: Xiao-Ping Zhang, Mita D. Desai and Ying-Ning Peng

Abstract: Recent wavelet research has primarily focused on real-valued
wavelet bases. However, complex wavelet bases offer a number of
potential advantages. For example, it has been recently suggested that
cite{Lawton93, Lina94} that the complex Daubechies wavelet can be
made symmetric. However, these papers always imply that if the complex
basis has a symmetry property then it must exhibit linear phase as
well. In this paper we prove that a linear phase complex orthogonal
wavelet does not exist. We study the implications of symmetry and
linear phase for both complex and real-valued orthogonal wavelet
bases. As a by-product, we propose a method to obtain a complex
orthogonal wavelet basis having the symmetry property and
approximately linear phase. The numerical analysis of the phase
response of various complex and real Daubechies wavelets is
given. Both real and complex-symmetric orthogonal wavelet can only
have symmetric amplitude spectra. Often it is desired to have
asymmetric amplitude spectra for processing general complex
signals. So we propose a method to design general complex orthogonal
perfect reconstruct filter banks (PRFBs) by parametrizing scheme.
Design examples are given. It is shown that the amplitude spectra of
the general complex conjugate quadraure filters (CQFs) can be
asymmetric with respect the zero frequency. This method can be used to
choose optimal complex orthogonal wavelet basis for processing complex
signals such as in radar and sonar.

Note: submitted to IEEE Trans. on Signal Processing, Special Issue on
Filter banks and wavelets.

A copy can be downloaded from

or Email to



Xiaoping Zhang
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