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| Titel:
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Density of Gabor Frames |
| Type:
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Journal articleJournal article |
| Person(er):
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Technical University of Denmark
Email:
Forfatter:
Heil, Christopher
Technical University of Denmark
Forfatter:
Deng, Baiqiao
Technical University of Denmark
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| Uddrag:
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A Gabor system is a set of time-frequency shifts S(g, Lambda) = {e(2 pi ibx) g(x - a)}((a,b)is an element of Lambda) of a function g is an element of L-2(R-d). We prove that if a finite union of Gabor systems boolean (ORk=1S)-S-r(g(k), Lambda(k)) forms a frame for L-2(R-d) then the lower and upper Beurling densities of Lambda = boolean ORk=1r Lambda(k) satisfy D- (Lambda) greater than or equal to 1 and D+(Lambda) < infinity. This extends recent work of Ramanathan and Steger. Additionally, we prove the conjecture that no collection boolean ORk=1r {g(k)(x - a)}(a is an element of Gamma k) of pure translates can form a frame for L-2 (R-d). (C) 1999 Academic Press. |
| Publiceret:
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in journal: Applied and Computational Harmonic Analysis (ISSN: 1063-5203) (DOI: http://dx.doi.org/10.1006/acha.1999.0271), vol: 7, issue: 3, pages: 292-304, 1999 |
| DOI:
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