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

• Published in: The Journal of fourier analysis and applications Vol. 18; no. 3; pp. 456 - 470
• Main Author: Søndergaard, Peter L.
• Format: Journal Article
• Language: English
• Published: Boston SP Birkhäuser Verlag Boston 01.06.2012; Springer
• Subjects: Abstract Harmonic Analysis; Algorithms; Analysis; Approximations and Expansions; Fourier Analysis; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Signal,Image and Speech Processing; Discrete Gabor Transform; 42C40; Algorithm; 42C15; Implementation
• ISSN: 1069-5869; 1531-5851
• DOI: 10.1007/s00041-011-9210-5

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.