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Excesses of Gabor frames

✍ Scribed by Radu Balan; Peter G. Casazza; Christopher Heil; Zeph Landau

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 186 KB
Volume: 14
Category: Article
ISSN: 1063-5203
DOI: 10.1016/s1063-5203(03)00006-x

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✦ Synopsis

A Gabor system for L 2 (R d ) has the form G(g, Λ) = {e 2πibx g(xa)} (a,b)∈Λ , where g ∈ L 2 (R d ) and Λ is a sequence of points in R 2d . We prove that, with only a mild restriction on the generator g and for nearly arbitrary sets of time-frequency shifts Λ, an overcomplete Gabor frame has infinite excess, and in fact there exists an infinite subset that can be removed yet leave a frame. The proof of this result yields an interesting connection between the density of Λ and the excess of the frame.

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