Multidimensional random process synthesis and simulation

In the paper, wide-sense stationary M-D (multidimensional) random processes, defined by their power spectral densities, are synthesised and simulated by using as an approximation M-D multisine random processes consisting of a sum of M-D sine components with deterministic amplitudes and random phase shifts. On the basis of the power spectral density function and phase shifts chosen with some well defined random properties the finite discrete Fourier transform of the M-D multisine random process is synthesized. The corresponding M-D multisine random process approximation is simulated by performing an inverse M-D finite Fourier transform of the synthesized spectrum. Realisations of the synthesised and simulated random process approximations may be obtained by using an M-D fast Fourier transform algorithm. The properties of synthesised M-D multisine random processes are discussed including M-D white multisine random process.