Abstract
Consider a bounded function g supported on [ − 1 , 1 ] and a modulation parameter b ∈ ] 1 / 2 , 1 [ for which the Gabor system { E m b T n g } m , n ∈ Z is a frame. We show that such a frame always has a compactly supported dual window. More precisely, we show that if b < N N + 1 for some N ∈ N , it is possible to find a dual window supported on [ − N , N ] . Under the additional assumption that g is continuous and only has a finite number of zeros on ] − 1 , 1 [ , we characterize the frame property of { E m b T n g } m , n ∈ Z . As a consequence we obtain easily verifiable criteria for a function g to generate a Gabor frame with a dual window having compact support of prescribed size.
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