Bandwidth Estimation in the Sampling Theorems
Tibor Poganj · 1992
The spectral representations of the Shannon-Kotelnikov sampling cardinal series expansion (SCSE) of non -bandlimited (NBL) stochastic signals were presented in some earlier papers by the author . This result gives the main tool in deriving the optimal value of the bandwidth in the approximation of the NBL stochastic signal by a sampling series of a BL signal such that it possesses the same spectral process . In this paper the Brown abasing error upper bound is extended to the NBL multidimensional stochastic processes and to the NBL homogeneous random fields . The magnitude of the derived bound is ordered under some smoothness condition upon the random field . Finally some statistical interpretations and methods are presented in the Shannon-Kotelnikov discretization procedure for the stochastic signals .