Using the DFT to synthesize multivariate orthogonal white noise series

A new type of generators for multivariate orthogonal white time-series is presented. It is based on defining their spectral representation in the form of discrete-frequency flat power spectrum densities with disjoint frequencies, which correspond in the time domain to a multivariate orthogonal multisine random time-series. The spectral representations are via inverse Fast Fourier Transform translated into the time domain resulting in multivariate orthogonal multisines with correlation properties like true orthogonal multivariate white noise series. This approach works perfectly for finite-time realization in case of scalar and bivariate orthogonal white noise time-series and results in asymptotically-white gaussian scalar or bivariate time-series and asymptotically-white multivariate orthogonal time-series for greater dimensions. However, all white time-series generated this way, even short ones, have very good correlation properties. The enhancement of the accuracy of simulated identification using those time-series is illustrated by a number of examples.