Random processes with specified spectral density and first-order probability density

The procedure for generating a Gaussian process with a specified spectral density is well known. It is harder to generate a process with a specified spectral density and a specified first-order probability distribution. In this paper we explore, by simulation, the possibility of generating a process with such a dual specification by passing a Gaussian process with an appropriately chosen spectral density through an appropriately chosen zero-memory nonlinearity. Several applications are cited where such a dual specification is desirable.