Proceedings PaperMatrix reformulation of the Gabor transform
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We have observed that if one restricts the von Neumann lattice to N points on the time axis and M points in the frequency axis there are, by definition, only MN independent Gabor coefficients. If the data is sampled such that there are exactly MN samples, then the forward and inverse Gabor transforms should be representable as linear transformations in CMN, the MN-dimensional vector space over the complex numbers, and the relationships that hold become matrix equations. These matrix equations are formulated, and some conclusions are drawn about the relative merits of using some methods as opposed to others, i.e., speed versus accuracy, as well as whether or not the coefficients that are obtained via some methods are true Gabor coefficients.