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Note on B-splines, wavelet scaling functions, and Gabor frames

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4 Author(s)
Grochenig, K. ; Dept. of Math., Connecticut Univ., Storrs, CT, USA ; Janssen, A.J.E.M. ; Kaiblinger, N. ; Pfander, G.E.

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,b>0 has no lower frame bound larger than 0 if b=2,3,... and a>0. 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 a>0. 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,.

Published in:

Information Theory, IEEE Transactions on  (Volume:49 ,  Issue: 12 )

Date of Publication:

Dec. 2003

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