Modeling of the Vector of Samples of Stationary Random Processes in Digital Signal Processing Systems

Abstract— The article proposes a method of modeling random sequences composed of digital samples of stationary random processes with a given power spectral density (PSD) in systems with digital signal processing (DSP). The method takes into account the limitation of the signal spectrum by the input devices of DSP systems and the peculiarities of the transfer function representation using fast Fourier transform. Digital white noise with Gaussian or uniform distribution is taken as an initial process for modeling. It is shown that the PSD estimation of the sequences obtained as a result of modeling is unbiased and its mean value coincides with the samples of the initial PSD. The expression for calculation of the RMS error of the estimation is obtained.