Moving average restoration of band-limited signals from noisy observations

The purpose of this paper is to describe the extension of the Whittaker-Shannon sampling theorem to the reconstruction of band-limited 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 a new reconstruction algorithm based on moving average smoothing is proposed. The consistency of the algorithm is established and the rate of convergence is investigated.