Reconstruction algorithm of signals from special samples in spline spaces
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
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Let g be a continuous, compactly supported function on such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g,a,b), with window g and time-shift and frequency-shift parameters a,b0 has no lower frame bound larger than 0 if b=2,3,... and a0. In particular, (g,a,b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b=2,3,... and a0. We give an example for our result for the case that g=B1, the triangle function supported by [-1,1], by showing pictures of the canonical dual corresponding to (g,a,b) where ab=1/4 and b crosses the lines N=2,3,.