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   -> Volume 6, Issue 6


Preprint: Asymptotic Convergence of the Dual Filter
 
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Author Message
Dong Wei (wei@vision.ece.utexas.edu)
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PostPosted: Tue Jun 10, 1997 4:36 am    
Subject: Preprint: Asymptotic Convergence of the Dual Filter
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#3 Preprint: Asymptotic Convergence of the Dual Filter

On Asymptotic Convergence of the Dual Filters Associated with Two
Families of Biorthogonal Wavelets

Dong Wei and Alan C. Bovik

Laboratory for Vision Systems
Department of Electrical and Computer Engineering
The University of Texas at Austin
Austin, TX 78712-1084, U.S.A.
E-mails: wei@vision.ece.utexas.edu, bovik@ece.utexas.edu

Abstract:

The asymptotic behavior of the dual filters associated with biorthogonal
spline wavelet (BSW) systems and general biorthogonal Coifman wavelet
(GBCW) systems are studied. As the order of the wavelet systems
approaches infinity, the magnitude responses of the dual filters in
the BSW systems either diverge or converge to some non-ideal frequency
responses. However, the synthesis filters in the GBCW systems
converge to an ideal halfband lowpass filter without exhibiting any
Gibbs-like phenomenon, and a subclass of the analysis filters also
converge to an ideal halfband lowpass filter but with a one-sided
Gibbs-like behavior. The two approximations of the ideal lowpass
filter by the filter associated with a Daubechies orthonormal wavelet
and by the synthesis filter in a GBCW system of the same order are
compared. Such a study of the asymptotic behaviors of wavelet systems
provides insightful characterization of these systems, and systematic
assessment and global comparison of different wavelet systems.

Web Site:

ftp://pepperoni.ece.utexas.edu/pub/GuestPut/convergence.ps.Z

Best regards,

Dong Wei

Laboratory for Vision Systems
Department of Electrical and Computer Engineering
The University of Texas at Austin
Austin, TX 78712-1084, U.S.A.
E-mails: wei@vision.ece.utexas.edu
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