On certain correlation properties of the sampling cardinal series expansion of stationary stochastic processes (Q2785622)

This paper is mainly concerned with finding upper bounds for the mean-square aliasing error. One of the most important results states that the mean-square aliasing error made to approximate a non band-limited weakly stationary (BL WS) process \(X\) by its sampling cardinal series expansion (SCSE) is upper bounded by \(4(\sigma^2- F(w)+ F(-w))\) if the spectral distribution function \(F\) of \(X\) is continuous at \((2k+1)w\), \(k\in\mathbb{Z}\), with some positive bandwidth. To arrive this inequality, the author processes spectral representations for the SCSE and for its correlation function as well. Next, a necessary and sufficient condition for two SCSE to be stationarily correlated is given, preparing in this way the discussion for the multidimensional case. Spectral representations and inequalities for the aliasing error are extended to the multidimensional case and, finally, the problem of controlling the mean-square aliasing error by chasing an optimal bandwidth is solved via inequalities of the above type.