Generation of Two Correlated Stationary Gaussian Processes

Since correlated stochastic processes are often presented in practical problems, feasible methods to model and generate correlated processes appropriately are needed for analysis and simulation. The present paper systematically presents three methods to generate two correlated stationary Gaussian processes. They are (1) the method of linear filters, (2) the method of series expansion with random amplitudes, and (3) the method of series expansion with random phases. All three methods intend to match the power spectral density for each process but use information of different levels of correlation. The advantages and disadvantages of each method are discussed.

Automated summary

This paper systematically presents three methods to generate two correlated stationary Gaussian processes, including the method of linear filters, the method of series expansion with random amplitudes, and the method of series expansion with random phases. These methods aim to match the power spectral density for each process with different levels of correlation information. The advantages and disadvantages of each method are discussed.