On perturbations of irregular Gabor frames

  • Authors:

  • Joseph D. Lakey;Ying Wang

  • Affiliations:

  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM;Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
  • Year:
  • 2003

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Abstract

We give a new sufficient condition under which an irregular Gabor system {eπipλxψ(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.