Gabor frames by sampling and periodization

Peter Lempel Søndergaard

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    By sampling the window of Gabor frame for L-2 (R) belonging to Feichtingers algebra S-0 (R), one obtains a Gabor frame for l(2) (Z). 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 L-2 (R), l(2) (Z), L-2 ([O,L]) and C-L. Some new results about the 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 L-2 (R).
    Original languageEnglish
    JournalAdvances in Computational Mathematics
    Issue number4
    Pages (from-to)355-373
    Publication statusPublished - 2007

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