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The probability density of the output of a filter when the input is a random telegraphic signal: Differential-equation method

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1 Author(s)

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, i.e., a random square wave with zeros obeying the Poisson distribution. 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 fordelta- functions at the edges. The applicability of this rectangular solution to other systems is investigated,

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Information Theory, IRE Transactions on  (Volume:5 ,  Issue: 5 )