Algorithm for Generating Samples of Homogeneous Gaussian Fields

A new algorithm is developed for generating samples of stationary Gaussian random fields. The algorithm is based on a model derived from the spectral representation theorem for weakly stationary random fields. The model consists of a superposition of a random number of waves with random amplitude and frequency, can match the second moment properties of any target random field, and becomes Gaussian as the intensity of two independent Poisson processes, defining the number of waves and their frequencies, increases indefinitely. In contrast to the current Monte Carlo simulation algorithms, the proposed algorithm: (1) does not produce periodic samples; and (2) does not require the discretization of the frequency domain. The proposed Monte Carlo algorithm is applied to generate samples of a stationary Gaussian field defined on ${ℝ}^2\text{.}$