Constructing super Gabor frames: the rational time-frequency lattice case

    Authors

    Z. Y. Li;D. G. Han

    Comments

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    Abbreviated Journal Title

    Sci. China-Math.

    Keywords

    super Gabor frame; orthonormal super frame; full rank lattice; tiles; HERMITE FUNCTIONS; REPRESENTATIONS; Mathematics, Applied; Mathematics

    Abstract

    For a time-frequency lattice I > = Aa"currency sign (d) x Ba"currency sign (d) , it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if vertical bar det(AB)vertical bar = 1/L. The proof of this result involves various techniques from multi-lattice tiling and operator algebra theory, and it is far from constructive. In this paper we present a very general scheme for constructing super Gabor frames for the rational lattice case. Our method is based on partitioning an arbitrary fundamental domain of the lattice in the frequency domain such that each subset in the partition tiles a"e (d) by the lattice in the time domain. This approach not only provides us a simple algorithm of constructing various kinds of orthonormal super Gabor frames with flexible length and multiplicity, but also allows us to construct super Gabor (non-Riesz) frames with high order smoothness and regularity. Several examples are also presented.

    Journal Title

    Science China-Mathematics

    Volume

    53

    Issue/Number

    12

    Publication Date

    1-1-2010

    Document Type

    Article

    Language

    English

    First Page

    3179

    Last Page

    3186

    WOS Identifier

    WOS:000285366000012

    ISSN

    1674-7283

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