Biorthogonal coiflets

Author

Cooklev, Todor ; Nishihara, A.

Author_Institution

Mobile Commun. Div., 3Com Corp., Salt Lake City, UT, USA

Volume

47

Issue

9

fYear

1999

fDate

9/1/1999 12:00:00 AM

Firstpage

2582

Lastpage

2588

Abstract

Coiflets are filter banks, where the sum of the number of vanishing moments of the analysis and synthesis limit functions is maximum for a given support width. It is known how to design biorthogonal coiflets with odd-length filters. However, the precise relationship among the vanishing moments of the analysis and synthesis scaling functions is unknown. This is the first problem solved in this correspondence. Second, biorthogonal coiflets with even length filters, which have remained unknown previously, are designed and the relationship among the vanishing moments of the analysis and synthesis limit functions shown. A generalization of the Bernstein polynomial is advanced. Each of these two wavelet families is parametrized by three integers. The design is based on explicit formulae

Keywords

channel bank filters; filtering theory; polynomials; wavelet transforms; Bernstein polynomial; analysis limit functions; biorthogonal coiflets; even length filters; filter banks; odd-length filters; scaling functions; synthesis limit functions; vanishing moments; wavelet families; Adaptive signal processing; Biomedical signal processing; Compaction; Costs; Discrete wavelet transforms; Filter bank; Signal processing algorithms; Signal resolution; Time frequency analysis; Wavelet packets;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.782213

Filename

782213