Multiresolution analysis, its link to the discrete parameter wavelet transform, and its initialization

Author

Chan, Y.T. ; Ho, K.C.

Author_Institution

Dept. of Electr. & Comput. Eng., R. Mil. Coll. of Canada, Kingston, Ont., Canada

Volume

44

Issue

4

fYear

1996

fDate

4/1/1996 12:00:00 AM

Firstpage

1001

Lastpage

1006

Abstract

By establishing an equivalence between the discrete parameter (DP) wavelet transform and the multiresolution analysis (MRA) detail coefficients, a simple derivation of the two-scale wavelet equations is given. MRA computes the DP of a signal s(t) only if the MRA inputs s(n) are samples of the inner product of s(t) and the scaling function. This is seldom true in practice. A prefiltering of s(n), as an approximate initialization, is necessary to make the MRA detail coefficients closer to the DP coefficients. A new prefiltering scheme is proposed and shown to be effective in an example

Keywords

filtering theory; signal resolution; signal sampling; transforms; wavelet transforms; DP; MRA; approximate initialization; discrete parameter wavelet transform; inner product; multiresolution analysis detail coefficients; prefiltering; scaling function; two-scale wavelet equations; Chirp; Discrete wavelet transforms; Fourier transforms; Frequency; Interference; Multiresolution analysis; Signal analysis; Signal processing; Signal resolution; Wavelet analysis;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.492556

Filename

492556