A Composite Linear Model Generating A Stationary Stochastic Process With Given Bispectrum

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A composite linear model is proposed, which converts from non-Gaussian i.i.d. processes into a nOnGaussian stationary stochastic processes with given third-order cumulant spectrum and with white power spectrum. The design for the model is based on the fact that a type of finite-impulse-response linear system with non-Gaussian i.i.d. input process makes an output process whose third order autocorrelations exist only for special time lags. Arbitrary third order autocorrelation function can be obtained by some superposition of independent output processes of this type. Results of numerical experiments confirm this fact. This model requires at most 2L2+4L+1 input i.i.d. processes independent of one another, for the third order autocorrelation function with the largest time lag L. With sufficient large L, a process with desired bispectrum can be made by this model.

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