Theory of regular M-band wavelet bases

Author

Steffen, Peter ; Heller, Peter N. ; Gopinath, Ramesh A. ; Burrus, C.S.

Author_Institution

Inst. for Commun. Theory, Erlangen-Nurnberg Univ., Germany

Volume

41

Issue

12

fYear

1993

fDate

12/1/1993 12:00:00 AM

Firstpage

3497

Lastpage

3511

Abstract

Orthonormal M-band wavelet bases have been constructed and applied by several authors. This paper makes three main contributions. First, it generalizes the minimal length K-regular 2-band wavelets of Daubechies (1988) to the M-band case by deriving explicit formulas for K-regular M-band scaling filters. Several equivalent characterizations of K-regularity are given and their significance explained. Second, two approaches to the construction of the (M-1) wavelet filters and associated wavelet bases are described; one relies on a state-space characterization with a novel technique to obtain the unitary wavelet filters; the other uses a factorization approach. Third, this paper gives a set of necessary and sufficient condition on the M-band scaling filter for it to generate an orthonormal wavelet basis. The conditions are very similar to those obtained by Cohen (1990) and Lawton (1990) for 2-band wavelets

Keywords

digital filters; filtering and prediction theory; signal processing; state-space methods; wavelet transforms; K-regular M-band scaling filters; minimal length K-regular 2-band wavelets; necessary condition; orthonormal M-band wavelet bases; regular M-band wavelet bases; state-space characterization; sufficient condition; unitary wavelet filters; Bandwidth; Channel bank filters; Compaction; Filter bank; Narrowband; RF signals; Radio frequency; Signal analysis; Signal processing; Sufficient conditions;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.258088

Filename

258088