Multiwavelet moments and projection prefilters

Author

Johnson, Bruce R.

Author_Institution

Dept. of Chem., Rice Univ., Houston, TX, USA

Volume

48

Issue

11

fYear

2000

fDate

11/1/2000 12:00:00 AM

Firstpage

3100

Lastpage

3108

Abstract

An efficient projection procedure is derived for use of orthogonal multiwavelets in the analysis of discrete data sequences. A family of simple prefilters corresponding to numerical quadrature evaluation of the projection integrals provides exact results for locally polynomial data. The full approximation order of the multiwavelet basis can thus always be enabled. For nonpolynomial signals, the prefilters provide approximations to the coefficients of the multiwavelet series whose convergence accelerates quickly with increase in sampling rate. Comparison is also made with previous time-invariant multiwavelet prefilters

Keywords

convergence of numerical methods; digital filters; integral equations; polynomial approximation; sequences; signal sampling; wavelet transforms; convergence; discrete data sequences; full approximation order; locally polynomial data; multiwavelet basis; multiwavelet moments; multiwavelet series; nonpolynomial signals; numerical quadrature evaluation; orthogonal multiwavelets; projection integrals; projection prefilters; projection procedure; sampling rate; time-invariant multiwavelet prefilters; Acceleration; Chemistry; Convergence; Convolution; Data analysis; Equations; Multiresolution analysis; Polynomials; Sampling methods; Signal resolution;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.875467

Filename

875467