Gabor frames by sampling and periodization |
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Authors: | Peter L. Søndergaard |
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Affiliation: | (1) Department of Mathematics, Technical University of Denmark, Building 303, 2800 Lyngby, Denmark |
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Abstract: | By sampling the window of a Gabor frame for belonging to Feichtinger’s algebra, , one obtains a Gabor frame for . In this article we present a survey of results by R. Orr and A.J.E.M. Janssen and extend their ideas to cover interrelations among Gabor frames for the four spaces , , and . Some new results about general dual windows with respect to sampling and periodization are presented as well. This theory is used to show a new result of the Kaiblinger type to construct an approximation to the canonical dual window of a Gabor frame for . |
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Keywords: | Gabor systems frames sampling periodization Poisson summation |
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