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Perturbation of wavelet and Gabor frames

✍ Scribed by Ivana Carrizo; Sergio Favier

Publisher: Springer
Year: 2003
Tongue: English
Weight: 608 KB
Volume: 19
Category: Article
ISSN: 1573-8175
DOI: 10.1007/bf02835283

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📜 SIMILAR VOLUMES

Irregular wavelet/Gabor frames

✍ Wenchang Sun; Xingwei Zhou 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 150 KB

We study the construction of wavelet and Gabor frames with irregular time-scale and timefrequency parameters, respectively. We give simple and sufficient conditions which ensure an irregular discrete wavelet system or Gabor system to be a frame. Explicit frame bounds are given. We also study the sta

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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 + ( ) < ∞.

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

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✍ 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