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The Mystery of Gabor Frames

✍ Scribed by Gröchenig, Karlheinz

Book ID
125338617
Publisher
SP Birkhäuser Verlag Boston
Year
2014
Tongue
English
Weight
585 KB
Volume
20
Category
Article
ISSN
1069-5869

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📜 SIMILAR VOLUMES

Excesses of Gabor frames
Excesses of Gabor frames
✍ Radu Balan; Peter G. Casazza; Christopher Heil; Zeph Landau 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 186 KB

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 infinit

Density of Gabor Frames
Density of Gabor Frames
✍ Ole Christensen; Baiqiao Deng; Christopher Heil 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 125 KB

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 + ( ) < ∞.

On the Stability of Gabor Frames
On the Stability of Gabor Frames
✍ Wenchang Sun; Xingwei Zhou 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 106 KB

In this paper, we study the stability of Gabor frames ϕ mb na m n ∈ Z . We show that ϕ mb na m n ∈ Z remains a frame under a small perturbation of ϕ m, or n. Our results improve some results from Favier and Zalik and are applicable to many frequently used Gabor frames. In particular, we study the ca