A new design algorithm for two-band orthonormal rational filter banks and orthonormal rational wavelets

Author

Blu, Thierry

Author_Institution

Swiss Fed. Inst. of Technol., Lausanne, Switzerland

Volume

46

Issue

6

fYear

1998

fDate

6/1/1998 12:00:00 AM

Firstpage

1494

Lastpage

1504

Abstract

We present a new algorithm for the design of orthonormal two-band rational filter banks. Owing to the connection between iterated rational filter banks and rational wavelets, this is also a design algorithm for orthonormal rational wavelets. It is basically a simple iterative procedure, which explains its exponential convergence and adaptability under various linear constraints (e,g., regularity). Although the filters obtained from this algorithm are suboptimally designed, they show excellent frequency selectivity. After an in-depth account of the algorithm, we discuss the properties of the rational wavelets generated by some designed filters. In particular, we stress the possibility to design “almost” shift error-free wavelets, which allows the implementation of a rational wavelet transform

Keywords

FIR filters; band-pass filters; convergence of numerical methods; digital filters; filtering theory; iterative methods; network synthesis; wavelet transforms; FIR filters; design algorithm; exponential convergence; frequency selectivity; iterated rational filter banks; linear constraints; orthonormal rational wavelets; rational wavelet transform; regularity; shift error-free wavelets; two-band orthonormal rational filter banks; Algorithm design and analysis; Channel bank filters; Convergence; Filter bank; Finite impulse response filter; Frequency; Information analysis; Iterative algorithms; Stress; Wavelet transforms;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.678463

Filename

678463