6533b7d3fe1ef96bd125ff5a

RESEARCH PRODUCT

A Linear Cost Algorithm to Compute the Discrete Gabor Transform

Miguel Arevalillo-herráezWladimiro Diaz-villanuevaSalvador Moreno-picot

subject

Matrix (mathematics)Signal ProcessingGabor waveletShort-time Fourier transformGabor transformElectrical and Electronic EngineeringAlgorithmSparse matrixMathematicsMatrix decompositionCholesky decompositionTime–frequency analysis

description

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.

yearjournalcountryeditionlanguage
2010-05-01IEEE Transactions on Signal Processing
https://doi.org/10.1109/tsp.2010.2043137