Title

On Fourier transforms of wavelet packets

Authors

Authors

K. Ahmad; R. Kumar;L. Debnath

Abbreviated Journal Title

Z. Anal. ihre. Anwend.

Keywords

wavelet packets; multi-resolution analysis; Fourier transform; quadrature mirror filter; ORTHONORMAL BASES; MULTIRESOLUTION; Mathematics, Applied; Mathematics

Abstract

This paper deals with the Fourier transform <()over cap>(n), of wavelet packets omega (n) is an element of L-2(R) relative to the scaling function phi = omega (o). Included there are proofs of the following statements: (i) <()over cap>n(0) = 0 for all n is an element of N. (ii) <()over cap>(n) (4nk pi) = 0 for all k is an element of Z, n = 2(j) for some j is an element ofN(o), provided \<()over cap>\,\m(o)\ are continuous. (iii) \<()over cap>(n)(xi)\(2) = Sigma (2r-1)(s=0)\<()over cap>(2rn+s)(2(r)xi)\(2) for r is an element of N. (iv) Sigma (infinity)(j=1) Sigma (2r-1)(s=0)Sigma (k is an element ofZ)\<()over cap>(n)(2(j+r)(xi +2k pi))\(2) = 1 for a.a. xi is an element of R where r = 1,2,...,j. Moreover, several theorems including a result on quadrature mirror filter are proved by using the Fourier transform of wavelet packets.

Journal Title

Zeitschrift Fur Analysis Und Ihre Anwendungen

Volume

20

Issue/Number

3

Publication Date

1-1-2001

Document Type

Article

Language

English

First Page

579

Last Page

588

WOS Identifier

WOS:000171852000003

ISSN

0232-2064

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