Abstract
In a previous note 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 (Grochenig et al. in IEEE Trans Inform Theory 49:3318–3320, 2003). 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 Heil and Walnut.
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