Sampling Representations and Approximations for Certain Functions and Stochastic Processes

摘要

Sampling representations and approximations of deterministic and random signals are important in communication and information theory. Finite sampling approximations are derived for certain functions and processes which are not bandlimited, as well as bounds on the approximation errors. Also derived are sampling representations for bounded linear operators acting on certain classes of bandlimited functions and processes; these representations enable one to reconstruct the image of a function (or a process) under a bounded linear operator using the samples of the image. Finally, sampling representations for distributions and random distributions are obtained. (Author)