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Abstract
The Gabor expansion of a function f (x) decomposes it into a double sum over integers m and n of a product of basis functions g(x−mX) and Fourier-series exponentials exp(2πin/X) for given spacing X. The choice of basis function determines the coefficients amn of the expansion. If f (x) is band limited, the double sum can for all practical purposes be replaced by a single sum over Gaussian basis functions. This is extremely useful for expansion of multidimensional functions such as beams in phase space. Conditions of validity are given, and several examples illustrate the technique.
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