On the Stability of Gabor Frames

Abstract

In this paper, we study the stability of Gabor frames {φmb,na:m,n∈Z}. We show that {φmb,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 case for which φ is not compactly supported, and, for the particular case of the Gaussian function, we give explicit stability bounds. © 2001 Academic Press.