On the distribution and moments of -filtered hard-limited -filtered white noise

Suppose white noise is put into an filter with time constant whose output is hard limited and fed into a second filter with time constant . The density of the output of the system has been the subject of several investigations. Most recently, Pawula and Tsai made the conjecture that for Gaussian white noise the density is given by a certain expression, a special case of which was derived earlier by Doyle, McFadden, and Marx for . In this paper an expression for the th moment of is found. From the expression for the fourth moment, it is proven that the Pawula-Tsai conjecture is not true in general. It is further found that if the output of the hard limiter were wide-sense Markov, the Pawula-Tsai conjecture would be true.