Probability Density of the Click Duration in an Ideal FM Discriminator

Abstract
The expression of the probability density function PClick(T) of the duration r of the clicks is determined as a function of 1) the expected number of clicks per second, Felick 2) the expected number of times per second that the noise component x(t) in phase with the carrier has instantaneous amplitude larger than that of the carrier itself 3) the probability density function peross(T) of the duration of the time intervals in which x(t) < -A 4) the probability that the values of the noise component in quadrature with the carrier will be of opposite sign at the extremes of time intervals of duration v. Using for Pcross(T) an approximate formula that holds fairly well in the range of the values of the signal-to-noise power ratio α usually encountered, PIick(T) has been calculated for several values of a and for two shapes of the noise spectrum, Gaussian and rectangular. Finally, an expression is given for the mean value of T.

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