Title

Frames, modular functions for shift-invariant subspaces and FMRA wavelet frames

Authors

Authors

Q. Gu;D. G. Han

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

Abbreviated Journal Title

Proc. Amer. Math. Soc.

Keywords

wavelet; wavelet frame; frame multiresolution analysis; shift-invariant; subspace; dimension function; DIMENSION FUNCTION; MULTIRESOLUTION ANALYSES; L(2)(R(D)); BASES; Mathematics, Applied; Mathematics

Abstract

We introduce the concept of the modular function for a shift-invariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and the multiplicity functions for general multiresolution analysis (GMRA). Given a frame mutiresolution analysis (FMRA), we show that the standard construction formula for orthonormal multiresolution analysis wavelets does not yield wavelet frames unless the underlying FMRA is an MRA. A modified explicit construction formula for FMRA wavelet frames is given in terms of the frame scaling functions and the low-pass filters.

Journal Title

Proceedings of the American Mathematical Society

Volume

133

Issue/Number

3

Publication Date

1-1-2005

Document Type

Article

Language

English

First Page

815

Last Page

825

WOS Identifier

WOS:000225333300025

ISSN

0002-9939

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