Gabor windows supported on [-1,1] and compactly supported dual windows

摘要

Consider a bounded function g supported on [-1,1] and a modulation parameter b ∈ ]1/2,1[ for which the Gabor system {E_(mb)T_ng}_(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+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_(mb)T_ng}_(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.