Efficient Algorithms for the Discrete Gabor Transform with a Long Fir Window

Peter Lempel Søndergaard

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

The Discrete Gabor Transform (DGT) is the most commonly used signal transform for signal analysis and synthesis using a linear frequency scale. The development of the Linear Time-Frequency Analysis Toolbox (LTFAT) has been based on a detailed study of many variants of the relevant algorithms. As a side result of these systematic developments of the subject, two new methods are presented here. Comparisons are made with respect to the computational complexity, and the running time of optimised implementations in the C programming language. The new algorithms have the lowest known computational complexity and running time when a long FIR window is used. The implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis.
Original languageEnglish
JournalJournal of Fourier Analysis and Applications
Volume18
Issue number3
Pages (from-to)456-470
ISSN1069-5869
DOIs
Publication statusPublished - 2012

Keywords

  • MATHEMATICS
  • FAST FOURIER-TRANSFORM
  • ZAK TRANSFORM
  • PHASE VOCODER
  • IMPLEMENTATION
  • SIGNALS
  • DESIGN
  • SERIES
  • Discrete Gabor Transform
  • Algorithm
  • Implementation

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