✦ LIBER ✦

Density of Gabor Frames

✍ Scribed by Ole Christensen; Baiqiao Deng; Christopher Heil

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 125 KB
Volume: 7
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.1999.0271

No coin nor oath required. For personal study only.

✦ Synopsis

A Gabor system is a set of time-frequency shifts S(g, ) = {e 2πibx g(xa)} (a,b)∈ of a function g ∈ L 2 (R d ). We prove that if a finite union of Gabor systems r k=1 S(g k , k ) forms a frame for L 2 (R d ) then the lower and upper Beurling densities of = r k=1 k satisfy D -( ) ≥ 1 and D + ( ) < ∞. This extends recent work of Ramanathan and Steger. Additionally, we prove the conjecture that no collection r k=1 {g k (xa)} a∈ k of pure translates can form a frame for L 2 (R d ).

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