Title

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

Authors

Authors

Z. Y. Li;D. G. Han

Comments

Authors: contact us about adding a copy of your work at STARS@ucf.edu

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

Share

COinS