Distribution of Click Amplitudes

The amplitude of a click is defined as the output of an ideal FM demodulator at the time of occurrence of the click. It is shown that the amplitude of a click (when the carrier is unmodulated) is a function of two random variables whose join distribution function is derived under the condition that a positive click has occurred. The distribution of positive click amplitudes is derived with the carrier-to-noise power ratio (CNR) at the output of the intermediate frequency (IF) filter as a parameter The results are extended to include negative clicks. The probability density and distribution functions of click amplitudes are plotted for the special case of a rectangular IF and CNRs of 4 and 9 The effect of modulation on the distribution of click amplitudes is determined. Results are given for the special case of a sinusoidal modulating signal fully deviating the carrier and a rectangular IF