Encyclopedia of Applied and Computational Mathematics

2015 Edition
| Editors: Björn Engquist

Gabor Analysis and Algorithms

  • Hans Georg Feichtinger
  • Franz Luef
Reference work entry
First Online:
DOI: https://doi.org/10.1007/978-3-540-70529-1_354
How to cite

Mathematics Subject Classification

Primary 42C15; 42B35

12

Keywords and Phrases

Gabor frames; Janssen representation; Time-frequency analysis

Motivation

Abstract harmonic analysis explains how to describe the (global) Fourier transform (FT) of signals even over general LCA (locally compact Abelian) groups but typically requires square integrability or periodicity. For the analysis of time-variant signals, an alternative is needed, the so-called sliding window FT or the STFT, the short-time Fourier transform, defined over phase space, the Cartesian, and the product of the time domain with the frequency domain. Starting from a signal f it is obtained by first localizing f in time using a (typically bump-like) window function g followed by a Fourier analysis of the localized part [1]. Another important application of time-frequency analysis is in wireless communication where it helps to design reliable mobile communication systems.

This article presents the key ideas of Gabor analysisas...

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Hans Georg Feichtinger
    • 1
  • Franz Luef
    • 2
  1. 1.Institute of Mathematics, University of ViennaViennaAustria
  2. 2.Department of Mathematics University of CaliforniaBerkeleyUSA