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Note on B-splines, wavelet scaling functions, and Gabor frames 总被引:3,自引:0,他引:3
Grochenig K. Janssen A.J.E.M. Kaiblinger N. Pfander G.E. 《IEEE transactions on information theory / Professional Technical Group on Information Theory》2003,49(12):3318-3320
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=B/sub 1/, 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,. 相似文献
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Acceleration of the frame algorithm 总被引:4,自引:0,他引:4
Shows how polynomial acceleration techniques which have been developed for the solution of large linear systems can be employed to improve and accelerate the frame algorithm. These methods permit a reduction in the number of necessary iterations by an order of magnitude when the frame algorithm is slow. The author gives several examples from the theory of irregular sampling, from wavelet theory and from Gabor theory where these methods are probably mandatory for efficient reconstruction 相似文献
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