Asymptotic convergence of biorthogonal wavelet filters

Author

Wei, Dong ; Bovik, Alan C.

Author_Institution

Dept. of Electr. & Comput. Eng., Texas Univ., Austin, TX, USA

Volume

2

fYear

1997

fDate

2-5 Nov. 1997

Firstpage

1244

Abstract

We study the asymptotic behavior of the dual filters associated with biorthogonal spline wavelets (BSWs) and general biorthogonal Coifman wavelets (GBCWs). As the order of wavelet systems approaches infinity the BSW filters either diverge or converge to some non-ideal filters, the GBCW synthesis filters converge to an ideal halfband lowpass (HBLP) filter without exhibiting any Gibbs-like phenomenon, and a subclass of the analysis filters also converge to an ideal HBLP filter but with a one-sided Gibbs-like behavior. The two approximations of the ideal HBLP filter by Daubechies orthonormal wavelet filters and by the GBCW synthesis filters are also compared.

Keywords

FIR filters; asymptotic stability; convergence of numerical methods; filtering theory; low-pass filters; wavelet transforms; Daubechies orthonormal wavelet filters; FIR filters; Gibbs-like phenomenon; analysis filters; asymptotic convergence; biorthogonal spline wavelets; biorthogonal wavelet filters; dual filters; general biorthogonal Coifman wavelets; ideal halfband lowpass filter; non-ideal filters; Convergence; Digital filters; Filter bank; Finite impulse response filter; Frequency; H infinity control; Laboratories; Spline; Transfer functions; Wavelet analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on

Conference_Location

Pacific Grove, CA, USA

ISSN

1058-6393

Print_ISBN

0-8186-8316-3

Type

conf

DOI

10.1109/ACSSC.1997.679103

Filename

679103