Gabor windows supported on [−1,1] and compactly supported dual windows
- Christensen, Ole
- Kim, Hong Oh
- Kim, Rae Young
DOIAbstract
AbstractConsider a bounded function g supported on [−1,1] and a modulation parameter b∈]1/2,1[ for which the Gabor system {EmbTng}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<NN+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 {EmbTng}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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