A linear cost algorithm to compute the discrete gabor transform

Authors:
Salvador Moreno-Picot;Miguel Arevalillo-Herráez;Wladimiro Díaz-Villanueva
Affiliations:
Computing Department, University of Valencia, Burjassot, Valencia, Spain;Computing Department, University of Valencia, Burjassot, Valencia, Spain;Computing Department, University of Valencia, Burjassot, Valencia, Spain
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

In this paper, we propose an alternative efficient method to calculate the Gabor coefficients of a signal given a synthesis window with a support of size much lesser than the length of the signal. The algorithm uses the canonical dual of the window (which does not need to be calculated beforehand) and achieves a computational cost that is linear with the signal length in both analysis and synthesis. This is done by exploiting the block structure of the matrices and using an ad hoc Cholesky decomposition of the Gabor frame matrix.