The Probability Density of the Output of a Filter When the Input is a Random Telegraphic Signal: Differential-Equation Method
Author:
- J. McFaddenJMJ. McFadden
- 1 May 1959
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 6 (5) , 228-233
Abstract
By the method of Darling and Siegert, a differential equation is obtained for the characteristic function of the output of a linear system when the input is a random telegraphic signal. For the ideal integrator with finite memory and for the RC low-pass filter, the solutions agree with previous results. For a truncated exponential weighting function, the characteristic function is obtained in terms of Bessel functions. For a particular ratio of the constants, the probability density of the output is rectangular except for delta functions. The applicability of this rectangular solution to other systems is investigated.Keywords
This publication has 2 references indexed in Scilit:
- Probability Densities of the Smoothed ‘ Random Telegraph Signal ’†Journal of Electronics and Control, 1958
- ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATIONQuarterly Journal of Mechanics and Applied Mathematics, 1951