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

    Authors

    Q. Gu;D. G. Han

    Comments

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    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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