License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.08492.4
URN: urn:nbn:de:0030-drops-18848
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/1884/
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Krahmer, Felix ; Pfander, Götz E. ; Rashkov, Peter

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

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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.


BibTeX - Entry

@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/opus/volltexte/2009/1884},
  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.}
}

Keywords: Gabor systems, erasure channels, time--frequency dictionaries, short--time Fourier transform, uncertainty principle.
Collection: 08492 - Structured Decompositions and Efficient Algorithms
Issue Date: 2009
Date of publication: 24.02.2009

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