A method with error estimates for band-limited signal extrapolation from inaccurate data

In this paper, we consider the problem of extrapolation of a band-limited signal outside a fixed interval from its (approximate or contaminated) values in that interval. We propose a new extrapolation method that estimates the error between the extrapolated and true values, and which also resolves the ill-posedness of the problem. The method is called a modified minimum norm solution (MMNS) method. Both the continuous MMNS and its discretization are studied. The error estimates hold for some classes of band-limited signals, when the maximum magnitude of the data error is known. These classes of band-limited signals are also characterized.

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