A decay result for certain windows generating orthogonal Gabor bases

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Abstract

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 1/2,1/2, in [0,1)2. 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, Gadzinski, and Powell, case p=q=2, on sharpness of the Balian-Low theorem.
Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalJournal of Fourier Analysis and Applications
Volume14
Issue number1
DOIs
Publication statusPublished - 2008

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