DISCRETE GABOR FRAMES IN l(2)(Z(d))

    Authors

    J. Lopez;D. G. Han

    Comments

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    Abbreviated Journal Title

    Proc. Amer. Math. Soc.

    Keywords

    Frames; discrete Gabor frames; Weyl-Heisenberg frames; TRANSFORMS; REPRESENTATIONS; DUALS; Mathematics, Applied; Mathematics

    Abstract

    The theory of Gabor frames for the infinite dimensional signal/function space L-2(R-d) and for the finite dimensional signal space R-d (or C-d) has been extensively investigated in the last twenty years. However, very little has been done for the Gabor theory in the infinite dimensional discrete signal space l(2)(Z(d)), especially when d > 1. In this paper we investigate the general theory for discrete Gabor frames in l(2)(Z(d)). We focus on a few fundamental aspects of the theory such as the density/incompleteness theorem for frames and super-frames, the characterizations for dual frame pairs and orthogonal (strongly disjoint) frames, and the existence theorem for the tight dual frame of the Gabor type. The existence result for Gabor frames (resp. super-frames) requires a generalization of a standard result on common subgroup coset representatives.

    Journal Title

    Proceedings of the American Mathematical Society

    Volume

    141

    Issue/Number

    11

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    3839

    Last Page

    3851

    WOS Identifier

    WOS:000326577500014

    ISSN

    0002-9939

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