A model for generating samples of stationary Gaussian processes

The generation of samples of stationary Gaussian processes is typically based on the spectral representation and the sampling theorems. The Monte Carlo simulation models based on the spectral representation theorem are most frequently used although they produce periodic samples whose period depends on the discretization of the frequency band of the process. This paper presents a new model for generating samples of stationary Gaussian processes that is based on the spectral representation theorem but does not yield periodic samples. The proposed model consists of a superposition of harmonics with random amplitude, phase, and frequency so that different samples have different periods. The proposed Monte Carlo algorithm is illustrated by an example involving a band limited Gaussian white noise process.