A remark on vanishing moments

Author

Tian, Jun ; Wells, Raymond O., Jr.

Author_Institution

Comput. Math. Lasb., Rice Univ., Houston, TX, USA

fYear

1996

fDate

3-6 Nov. 1996

Firstpage

983

Abstract

It is well known that with more vanishing moments on the scaling function and the wavelet function, one may get a better wavelet sampling approximation. In this paper, we present a quantitative treatment of the above statement. It is shown that equal vanishing moments distribution between the scaling function and the wavelet function is an ideal choice for the wavelet sampling approximation. Based on this observation, we introduce biorthogonal Coifman wavelet systems, a family of biorthogonal wavelet systems with the vanishing of moments equally distributed between scaling functions and wavelet functions. These wavelet systems provide a good wavelet sampling approximation with exponential decay, and the scaling vectors are all dyadic rational.

Keywords

approximation theory; signal sampling; wavelet transforms; biorthogonal Coifman wavelet systems; dyadic rational scaling vectors; exponential decay; scaling function; vanishing moments; wavelet function; wavelet sampling approximation; Laboratories; Mathematics; Sampling methods; Wavelet analysis;

fLanguage

English

Publisher

ieee

Conference_Titel

Signals, Systems and Computers, 1996. Conference Record of the Thirtieth Asilomar Conference on

Conference_Location

Pacific Grove, CA, USA

ISSN

1058-6393

Print_ISBN

0-8186-7646-9

Type

conf

DOI

10.1109/ACSSC.1996.599091

Filename

599091