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Generation of Two Correlated Stationary Gaussian Processes

期刊

MATHEMATICS
卷 9, 期 21, 页码 -

出版社

MDPI
DOI: 10.3390/math9212687

关键词

correlated stochastic processes; liner filters; series expansion; random amplitudes; random phases; simulations

资金

  1. National Natural Science Foundation of China [11772293, 12172323]

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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.
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.

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