Title

Frames, Modular Functions For Shift-Invariant Subspaces And Fmra Wavelet Frames

Keywords

Dimension function; Frame multiresolution analysis; Shift-invariant subspace; Wavelet; Wavelet frame

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. © 2004 American Mathematical Society.

Publication Date

3-1-2005

Publication Title

Proceedings of the American Mathematical Society

Volume

133

Issue

3

Number of Pages

815-825

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-04-07601-4

Socpus ID

14644392169 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/14644392169

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