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An open question on the existence of Gabor frames in general linear position

Authors: Felix Krahmer, Götz E. Pfander, and Peter Rashkov

Published in: Dagstuhl Seminar Proceedings, Volume 8492, Structured Decompositions and Efficient Algorithms (2009)

Abstract

Uncertainty principles for functions defined on finite Abelian groups generally relate the cardinality of a function to the cardinality of its Fourier transform. We examine how the cardinality of a function is related to the cardinality of its short--time Fourier transform. We illustrate that for some cyclic groups of small order, both, the Fourier and the short--time Fourier case, show a remarkable resemblance. We pose the question whether this correspondence holds for all cyclic groups.

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Felix Krahmer, Götz E. Pfander, and Peter Rashkov. An open question on the existence of Gabor frames in general linear position. In Structured Decompositions and Efficient Algorithms. Dagstuhl Seminar Proceedings, Volume 8492, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{krahmer_et_al:DagSemProc.08492.4,
  author =	{Krahmer, Felix and Pfander, G\"{o}tz E. and Rashkov, Peter},
  title =	{{An open question on the existence of Gabor frames  in general linear position}},
  booktitle =	{Structured Decompositions and Efficient Algorithms},
  pages =	{1--7},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8492},
  editor =	{Stephan Dahlke and Ingrid Daubechies and Michal Elad and Gitta Kutyniok and Gerd Teschke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08492.4},
  URN =		{urn:nbn:de:0030-drops-18848},
  doi =		{10.4230/DagSemProc.08492.4},
  annote =	{Keywords: Gabor systems, erasure channels, time--frequency dictionaries, short--time Fourier transform, uncertainty principle.}
}

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An open question on the existence of Gabor frames in general linear position

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