On certain correlation properties of the sampling cardinal series expansion of stationary stochastic processes

Tibor Pogány, Rijeka, Croatia

Keywords: Stationary stochastic processes, cardinal series, sampling, multidimensional processes, spectral representation, optimal bandwidth, Brown’s upper bound AMS Subject classification: 60G10, 60G99

Abstract: The spectral representation of the sampling cardinal series expansion (SCSE) of non bandlimited (BL) weakly stationary scalar and multidimensional stochastic processes and the correlation function of SCSE’s in both cases are derived. Mean-square aliasing error upper bounds are given for the multidimensional processes. These results give the main tool in deriving the optimal value of the bandwidth in the mean-square approximation of the non BL stochastic process by its SCSE.