Title

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

Authors

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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