A new method of random time-series simulation

A new approach to the simulation of wide-sense stationary random time-series, defined by its power spectral density, is presented. This approach is based on approximating the time-series nonparametric power spectral density representation by a periodogram of multisine random time-series. This periodogram is used to construct a discrete Fourier transform of the multisine random time-series. Application of any FFT algorithm to this discrete Fourier transform results in a multisine random time-series with the predefined spectrum. The properties of multisine random time-series obtained this way are discussed including their asymptotic gaussianess. The proposed approach is illustrated by examples that demonstrate better spectral and correlation properties of multisine simulated random processes in comparison with time-series simulated classically as the output of a linear filter excited by white noise.