Title

Constructing Super Gabor Frames: The Rational Time-Frequency Lattice Case

Keywords

full rank lattice; orthonormal super frame; super Gabor frame; tiles

Abstract

For a time-frequency lattice Λ = Aℤd × Bℤd, it is known that an orthonormal super Gabor frame of length L exists with respect to this lattice if and only if {pipe}det(AB){pipe} = 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 ℝd 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. © Science China Press and Springer-Verlag Berlin Heidelberg 2010.

Publication Date

12-1-2010

Publication Title

Science China Mathematics

Volume

53

Issue

12

Number of Pages

3179-3186

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11425-010-4109-1

Socpus ID

78650400307 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/78650400307

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