In a previous note K. Grochenig 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.
On a necessary condition for B-spline Gabor frames
DEL PRETE, VINCENZA
2010-01-01
Abstract
In a previous note K. Grochenig 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.File in questo prodotto:
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