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Gabor frames in finite dimensions


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Pfander, Götz E.:
Gabor frames in finite dimensions.
In: Casazza Peter K. ; Kutyniok Gitta (Hrsg): Finite Frames. - Boston : Birkhäuser, 2013. - S. 193-239. - (Applied and Numerical Harmonic Analysis)
ISBN 978-0-8176-8372-6 ; 978-0-8176-8373-3 ; 0-8176-8372-0


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Gabor frames have been extensively studied in time-frequency analysis over the last 30 years. They are commonly used in science and engineering to synthesize signals from, or to decompose signals into, building blocks which are localized in time and frequency. This chapter contains a basic and self-contained introduction to Gabor frames on finite-dimensional complex vector spaces. In this setting, we give elementary proofs of the central results on Gabor frames in the greatest possible generality; that is, we consider Gabor frames corresponding to lattices in arbitrary finite Abelian groups. In the second half of this chapter, we review recent results on the geometry of Gabor systems in finite dimensions: the linear independence of subsets of its members, their mutual coherence, and the restricted isometry property for such systems. We apply these results to the recovery of sparse signals, and discuss open questions on the geometry of finite-dimensional Gabor systems.

Weitere Angaben

Publikationsform:Aufsatz in einem Buch
Schlagwörter:Gabor analysis on finite Abelian groups; Linear independence; Coherence; Restricted isometry constants of Gabor frames; Applications to compressed sensing; Erasure channel error correction; Channel identification
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen
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DOI / URN / ID:10.1007/978-0-8176-8373-3_6
Begutachteter Aufsatz:Ja
Titel an der KU entstanden:Nein
Eingestellt am: 29. Aug 2017 08:22
Letzte Änderung: 29. Aug 2017 08:22
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