کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4590729 | 1334979 | 2013 | 20 صفحه PDF | دانلود رایگان |
The well known density theorem in time-frequency analysis establishes the connection between the existence of a Gabor frame G(g,A,B)={e2πi〈Bm,x〉g(x−An):m,n∈Zd}G(g,A,B)={e2πi〈Bm,x〉g(x−An):m,n∈Zd} for L2(Rd)L2(Rd) and the density of the time-frequency lattice AZd×BZdAZd×BZd. This is also tightly related to lattice tiling and packing. In this paper we investigate the density theorem for Gabor systems in L2(S)L2(S) with S being an AZdAZd-periodic subset of RdRd. We characterize the existence of a Gabor frame for L2(S)L2(S) in terms of a condition that involves the Haar measure of the group generated by AZdAZd and (Bt)−1Zd(Bt)−1Zd. This new characterization is used to recover the density theorem and several related known results in the literature. Additionally we apply this approach to obtain the density theorems for multi-windowed and super Gabor frames for L2(S)L2(S).
Journal: Journal of Functional Analysis - Volume 265, Issue 7, 1 October 2013, Pages 1170–1189