On the stability of Gabor frames

In this paper, we study the stability of Gabor frames {phi (mb, na) : m, n is an element of Z}. We show that {phi (mb, na) : m, n is an element of Z} remains a frame under a small perturbation of phi, m, or n. Our results imp rove some results from Favier and Zalik and are applicable to many frequent ly used Gabor frames. In particular, we study the case for which phi is not compactly supported, and, for the particular case of the Gaussian function , we give explicit stability bounds. (C) 2001 Academic Press.