Characterizations of tight over-sampled affine frame systems and over-sampling rates

    Authors

    C. K. Chui;Q. Y. Sun

    Comments

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    Abbreviated Journal Title

    Appl. Comput. Harmon. Anal.

    Keywords

    MAXIMUM VANISHING MOMENTS; COMPACTLY SUPPORTED TIGHT; WAVELET FRAMES; R-N; DILATIONS; L-2(R-D); Mathematics, Applied; Physics, Mathematical

    Abstract

    Let M be a dilation matrix, Psi a finite family of L-2-functions, and P the collection of all nonsingular matrices P such that M, P, and PMP-1 have integer entries. The objective of this paper is two-fold. First, for each P in P, we characterize all tight affine frames X (Psi, M) generated by Psi such that the over-sampled affine systems X (P) (Psi, M) relative to the "over-sampling rate" P remain to be tight frames. Second, we characterize all over-sampling rates P is an element of P, such that the over-sampled affine systems X (P) (Psi, M) are fight frames whenever the affine system X (Psi, M) is a tight frame. Our second result therefore provides a general and precise formulation of the second over-sampling theorem for tight affine frames. (C) 2006 Elsevier Inc. All rights reserved.

    Journal Title

    Applied and Computational Harmonic Analysis

    Volume

    22

    Issue/Number

    1

    Publication Date

    1-1-2007

    Document Type

    Article

    Language

    English

    First Page

    1

    Last Page

    15

    WOS Identifier

    WOS:000243607300001

    ISSN

    1063-5203

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