This is a paper on the discrete Gabor transform. We discuss the calculation of dual and tight Gabor atoms, for Gabor atoms which satisfy certain support restrictions related to the relevant time- and frequency lattice constants. These conditions imply that the Gabor frame operator is just a point-wise multiplication operator and therefore computing the inverse or the square root of the inverse frame operator are computationally inexpensive.

Keywords: Gabor analysis, numerical work

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