Neural pulse frequency modulation of an exponentially correlated Gaussian process

When the input to a Neural Pulse Frequency Modulation (NPFM) system is a stationary random process the output takes the form of a train of impulses for which the occurrence times and the intensities are stationary processes of a discrete type. Particularly, the impulse occurrence times constitute a stationary point process where the average impulse frequency (average number of impulses per unit time) becomes a reciprocal of the mean impulse period. Due to the inherent nature of the modulation procedure the determination of the mean impulse period transforms to a problem of computing the mean first passage time of a random process which is not necessarily Markovian. In this paper numerical solutions of the average impulse frequency of a Neural Pulse Frequency Modulation System are obtained for the case of an exponentially correlated Gaussian input. Monte Carlo computer simulations substantiate the theoretically obtained results.