An Efficient Method for the Fourier Transform of a Neuronal Spike Train

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Abstract
A spike train may be represented by a superposition of Dirac .delta.-functions. One of the simplest ways of converting such a comb function into a continuous function is to use a Fourier transform. In general there are 2 possibilities, both of which have their disadvantages: the direct transform which is extremely time-consuming and the fast Fourier transform of the low pass filtered comb function. The latter method, although quicker, often requires a greater storage capacity than is readily available. A 3rd possibility is suggested in this paper. Essentially, it is a direct Fourier transform which takes advantage of certain properties of a spike train. The corresponding algorithm works much faster than a common Fourier transform.

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