Università degli Studi di Genova

On a necessary condition for B-spline Gabor frames
Abstract: In a previous note K. Gr$\bf \rm{ \ddot{o}}$chenig et al. prove that if $g$ is a continuous function with compact support such that the translates of $g$ form a partition of unity, then $g$ cannot generate a Gabor frame for integer values of the frequency shift parameter $b$ greater than 1. We give a simpler proof of this result which applies also to windows $g$ which are neither continuous nor with compact support. Our proof is based on a necessary condition for Gabor frames due to C. E. Heil and D. F. Walnut. Keywords: Gabor frame, partition of unity, dual window, Ron-Shen condition, B-spline MSC: 42 Altre info:

On a necessary condition for B-spline Gabor frames