Multisine approximation of multivariate orthogonal random processes

A new approach to the synthesis and simulation of widesense stationary multivariate orthogonal random time-series defined by its power spectral density matrix is presented. This approach is based on approximating the time-series nonparametric power spectral density representation by a periodogram matrix of multivariate orthogonal multisine random time series. This periodogram matrix is used to construct a discrete Fourier transform vector of multivariate orthogonal multisine random time series. Application of any FFT algorithm to this discrete Fourier transform vector results in a multivariate orthogonal multisine random time series with the predefined spectrum. The properties of multivariate orthogonal multisine random time series obtained this way are discussed. Attention is given to asymptotic Gaussianity.