Gabor frames with rational density
Information Theory
2011-08-15 v1 math.IT
Abstract
We consider the frame property of the Gabor system G(g, {\alpha}, {\beta}) = {e2{\pi}i{\beta}nt g(t - {\alpha}m) : m, n \in Z} for the case of rational oversampling, i.e. {\alpha}, {\beta} \in Q. A 'rational' analogue of the Ron-Shen Gramian is constructed, and prove that for any odd window function g the system G(g, {\alpha}, {\beta}) does not generate a frame if {\alpha}{\beta} = (n-1)/n. Special attention is paid to the first Hermite function h_1(t) = te^(-{\pi}t^2).
Cite
@article{arxiv.1108.2684,
title = {Gabor frames with rational density},
author = {Yurii Lyubarskii and Preben Gråberg Nes},
journal= {arXiv preprint arXiv:1108.2684},
year = {2011}
}
Comments
13 pages, 2 figures