Title

Discrete Gabor Frames In ℓ2(ℤD)

Keywords

Discrete Gabor frames; Frames; Weyl-Heisenberg frames

Abstract

The theory of Gabor frames for the infinite dimensional signal/ function space L2(ℝd) and for the finite dimensional signal space Rd (or Cd) 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 ℓ2(ℤd), especially when d > 1. In this paper we investigate the general theory for discrete Gabor frames in ℓ2(ℤd). 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. © 2013 American Mathematical Society.

Publication Date

8-27-2013

Publication Title

Proceedings of the American Mathematical Society

Volume

141

Issue

11

Number of Pages

3839-3851

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1090/S0002-9939-2013-11875-7

Socpus ID

84882588290 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84882588290

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