Synthesis of random multivariate time series with exactly prescribed power spectral densities

Many engineering signals can be modeled as stationary random processes. The distributions of these signals are defined by covariance functions in the time domain and power spectral densities (PSDs) in the frequency domain. A common problem is to synthesize time series from a random model with desired autospectra, coherence, and phase across multiple signals. For a finite number of randomly sampled signal partitions, the calculated sample PSD does not generally match the distribution PSD. We describe a method for synthesizing waveforms with exactly prescribed auto- and cross-spectral densities. Furthermore, we prove that the random variable induced by the waveform generator is the closest in distribution to the original distribution among all random variables satisfying the PSD constraint. Numerical studies using a Gaussian model demonstrate convergence in practice, and the measured kurtosis and skewness of synthesized waveforms are similar to those obtained by Gaussian sampling. The synthesis method also improves control accuracy in a random vibration control simulation.