Theoretical duration and amplitude of an FM click (Corresp.)

The exact initial behavior of the probability density of the duration of an FM click in the case of an unmodulated carrier plus narrowband stationary Gaussian noise is presented. A simple Maxwell probability density is developed to approximate the probability density of the duration. The development leads to the conjecture that the Maxwell probability density is the exact limiting probability density of the duration as the carrier-to-noise power ratio approaches infinity. Analogous results are presented for the amplitude of an FM click. Simple formulas are developed for the mean, variance, and most probable value of the duration and amplitude of an FM click. It is shown that these theoretical developments yield numerical results which are in good agreement with many experimental and numerical results reported in the literature.