Moving average restoration of bandlimited signals from noisy observations

The purpose of this paper is to describe the extension of the Whittaker-Shannon sampling theorem to reconstruction of bandlimited functions in the presence of zero mean, uncorrelated noise. It is shown that the classical Whittaker-Shannon sampling scheme is not consistent in the case of noisy measurements, and new reconstruction algorithms based on the moving average smoothing are proposed. The weak and strong consistency of the algorithms is established, and the rate of convergence is investigated. The theory is verified in the computer simulations.