A decay result for certain windows generating orthogonal Gabor bases
نویسنده
چکیده
We consider tight Gabor frames (h, a = 1, b = 1) at critical density with h of the form Z−1(Zg/|Zg|). Here Z is the standard Zak transform and g is an even, real, well-behaved window such that Zg has exactly one zero, at ( 2 , 1 2 ), in [0, 1). We show that h and its Fourier transform have maximal decay as allowed by the Balian-Low theorem. Our result illustrates a theorem of Benedetto, Czaja, Gadziński, and Powell, case p = q = 2, on sharpness of the Balian-Low theorem. Math Subject Classifications (2000): 42C15, 42C25, 94A12.
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