Gabor frames with rational density
نویسندگان
چکیده
We consider the frame property of the Gabor system G(g, α, β) = {eg(t − αm) : m,n ∈ Z} for the case of rational oversampling, i.e. α, β ∈ Q. A ’rational’ analogue of the Ron-Shen Gramian is constructed, and prove that for any odd window function g the system G(g, α, β) does not generate a frame if αβ = n−1 n . Special attention is paid to the first Hermite function h1(t) = te −πt .
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ورودعنوان ژورنال:
- CoRR
دوره abs/1108.2684 شماره
صفحات -
تاریخ انتشار 2011