A stable Gabor-type representation of an image requires that the Zak transform (ZT) of the reference function does not vanish over the fundamental cube. We prove that the discrete ZT of any symmetric set of reference data points has a zero. To overcome the computational problem, which is due to the zero plane generated by the ZT of the Gaussian reference function, the Gaussian is translated by a sub-pixel distance. We show that the absolute value of the minimum of the ZT of the Gaussian is a function of the sub-pixel distance of translation and that the optimum value of such translation is 1/2 pixel.
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