On perturbations of irregular Gabor frames

Joseph D. Lakey; Ying Wang

doi:10.1016/S0377-0427(02)00895-6

On perturbations of irregular Gabor frames

Joseph D. Lakey, Ying Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We give a new sufficient condition under which an irregular Gabor system {e^2πipλxψ(x-q_λ)} forms a Bessel sequence for L²(ℝ). The Bessel bound just requires a mild decay on ψ. This condition then can be used to prove stability of an irregular Gabor frame under a perturbation of its generating function. We go on to outline how the perturbation result can be used to extend a sufficient condition of Heller for irregular Gabor frames with compactly supported generator to the case of a noncompactly supported generator.

Original language	English (US)
Pages (from-to)	111-129
Number of pages	19
Journal	Journal of Computational and Applied Mathematics
Volume	155
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(02)00895-6
State	Published - Jun 1 2003

Keywords

Gabor frames
Perturbation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(02)00895-6

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AB - We give a new sufficient condition under which an irregular Gabor system {e2πipλxψ(x-qλ)} forms a Bessel sequence for L2(ℝ). The Bessel bound just requires a mild decay on ψ. This condition then can be used to prove stability of an irregular Gabor frame under a perturbation of its generating function. We go on to outline how the perturbation result can be used to extend a sufficient condition of Heller for irregular Gabor frames with compactly supported generator to the case of a noncompactly supported generator.

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KW - Perturbation

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JO - Journal of Computational and Applied Mathematics

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On perturbations of irregular Gabor frames

Abstract

Keywords

ASJC Scopus subject areas

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