A simulation method for stationary Gaussian random functions based on the sampling theorem

Abstract

A unified method is developed for simulating realizations of real-valued stationary Gaussian processes, vector processes, fields, and vector fields. The method is based on parametric random models consisting of superpositions of deterministic functions of time or space with random amplitudes. The parametric models are based on the sampling theorem for random processes and generalizations of it for vector processes and random fields. The proposed simulation method is efficient and uses algorithms for generating realizations of random processes and fields that are similar to simulation techniques based on ARMA models. Several examples are presented to demonstrate the proposed simulation method and evaluate its efficiency and accuracy.