Regular Article: On the Stability of Gabor Frames

Authors:
Wenchang Sun;Xingwei Zhou
Affiliations:
Department of Mathematics, Nankai University, Tianjin, 300071, China;Department of Mathematics, Nankai University, Tianjin, 300071, China
Venue:
Advances in Applied Mathematics
Year:
2001

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Abstract

In this paper, we study the stability of Gabor frames {@f"m"b","n"a:m,n@?Z}. We show that {@f"m"b","n"a:m,n@?Z} remains a frame under a small perturbation of @f,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 @f is not compactly supported, and, for the particular case of the Gaussian function, we give explicit stability bounds.