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

Abstract

A spike train may be represented by a superposition of Dirac δ-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 two 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. In the present paper, therefore, a third possibility is suggested. 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.