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

Krahmer, Felix; Pfander, Götz E.; Rashkov, Peter

doi:10.4230/DagSemProc.08492.4

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

Authors Felix Krahmer, Götz E. Pfander, Peter Rashkov

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 8492
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2009-02-24

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DOI: 10.4230/DagSemProc.08492.4
URN: urn:nbn:de:0030-drops-18848

Subject Classification

Keywords

Gabor systems
erasure channels
time--frequency dictionaries
short--time Fourier transform
uncertainty principle.

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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.

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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) https://doi.org/10.4230/DagSemProc.08492.4

Author Details

Felix Krahmer

Götz E. Pfander

Peter Rashkov

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