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.
|Number of pages||15|
|Journal||Journal of Fourier Analysis and Applications|
|Publication status||Published - 2008|