On the spectral representation method in simulation

Abstract

Two models Xn(t) and Yn(t) are considered for generating samples of stationary band-limited Gaussian processes. The models are based on the spectral representation method and consist of a superposition of n harmonics. The harmonics of Xn(t) have random phase and amplitude while the harmonics of Yn(t) only have random phase. It is shown that the two models are equal in the second-moment sense. However, Yn(t) has stronger ergodic properties than Xn(t). On the other hand, Xn(t) is a Gaussian process for any value of n while Yn(t) is asymptotically Gaussian as n approaches infinity. It is demonstrated that the rejection of Xn(t), because of its weak ergodic property, or of model Yn(t), because of its nonGaussian distribution, it is not generally justified. One special case in which Yn(t) should not be used is that of Gaussian processes with power concentrated at a few discrete frequencies.

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