The fourth product moment of infinitely clipped noise

This paper considers the fourth product moment, w(τ1, τ2, τ3) = E[x(t)x(t + τ1)x(t + τ2)x(t + τ3)], when x(t) is infinitely clipped noise with a mean value of zero. If the noise is Gaussian before clipping, the moment w is not obtainable in closed form. For this reason, the Gaussian assumption is withdrawn and other assumptions are employed. If the zeros of x(t) obey the Poisson distribution, a particularly simple result follows for w and for all higher moments. An alternative assumption is the following. Let unspecified events occur at times τ0, τ1, τ2, … according to the Poisson distribution. If alternate events, i.e., those at τ1, τ3, τ5, …, are designated as the zeros of x(t), both the autocorrelation function and w(τ1, τ2, τ3) can be derived. The results are in terms of elementary functions. A comparison is made between these models and clipped Gaussian processes.