The theory and design of arbitrary-length cosine-modulated filter banks and wavelets, satisfying perfect reconstruction

Author

Nguyen, Truong Q. ; Koilpillai, R. David

Author_Institution

Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA

Volume

44

Issue

3

fYear

1996

fDate

3/1/1996 12:00:00 AM

Firstpage

473

Lastpage

483

Abstract

It is well known that FIR filter banks that satisfy the perfect-reconstruction (PR) property can be obtained by cosine modulation of a linear-phase prototype filter of length N=2mM, where M is the number of channels. In this paper, we present a PR cosine-modulated filter bank where the length of the prototype filter is arbitrary. The design is formulated as a quadratic-constrained least-squares optimization problem, where the optimized parameters are the prototype filter coefficients. Additional regularity conditions are imposed on the filter bank to obtain the cosine-modulated orthonormal bases of compactly supported wavelets. Design examples are given

Keywords

FIR filters; band-pass filters; delay circuits; digital filters; least squares approximations; modulation; optimisation; signal reconstruction; transforms; wavelet transforms; FIR filter banks; arbitrary-length cosine-modulated filter banks; design; linear-phase prototype filter; orthonormal bases; perfect reconstruction; prototype filter coefficients; quadratic-constrained least-squares optimization problem; regularity conditions; theory; wavelets; Channel bank filters; Design optimization; Filter bank; Finite impulse response filter; Image reconstruction; Lattices; Prototypes; Signal synthesis; Speech coding; Speech synthesis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.489021

Filename

489021