Probability Densities of the Smoothed ‘ Random Telegraph Signal ’†

ABSTRACT The problem treated is that of finding the probability distribution of the output from a simple resistance-capacity smoothing network when the input is a sequence of random square waves generated by a Poisson process. The moments of the first probability distribution are obtained and the density function derived. The results suggest a convenient experimental method for generating low frequency noise with Gaussian, rectangular, parabolic or elliptical probability density functions. An incidental result gives the higher-order autocorrelation functions of the random square-wave input.