Using the DFT to synthesize bivariate orthogonal white noise series

The discrete Fourier transform (DFT) is used to generate bivariate orthogonal series in the form of bivariate random-phase multisine series. The properties of those series are presented. The concept of N/2-lag white series is introduced as series whose ad function coincides with the ac function of white noise for lags 0, 1, ..., N/2-1. It is shown how to turn bivariate orthogonal multisine series into corresponding bivariate orthogonal N/2-lag white series and into asymptotically Gaussian bivariate orthogonal white series. The main part of the algorithm for generating such series via DFT is presented. The spectral, correlation, and Gaussian properties of the introduced series are illustrated by three numerical examples.