A. Krzyzak et al., MOVING AVERAGE RESTORATION OF BAND-LIMITED SIGNALS FROM NOISY OBSERVATIONS, IEEE transactions on signal processing, 45(12), 1997, pp. 2967-2976
The purpose of this paper is to describe the extension of the Whittake
r-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 consis
tency of the algorithms is established, and the rate of convergence is
investigated, The theory is verified in the computer simulations.