The fourth product moment of infinitely clipped noise

This paper considers the fourth product moment, w(τ 1 , τ 2 , τ 3 ) = E[x(t)x(t + τ 1 )x(t + τ 2 )x(t + τ 3 )], 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 For this reason, the Gaussian assumption is withdrawn and other assumptions are employed.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 τ 0 , τ 1 , τ 2 , … according to the Poisson distribution. If alternate events, i.e., those at τ 1 , τ 3 , τ 5 , …, are designated as the zeros of x(t), both the autocorrelation function and w(τ 1 , τ 2 , τ 3 ) can be derived. The results are in terms of elementary functions. A comparison is made between these models and clipped Gaussian processes.