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-limi ted signal outside a fixed interval from its (approximate or contamina ted) values in that interval. We propose a new extrapolation method th at estimates the error between the extrapolated and true values, and w hich also resolves the ill-posedness of the problem. The method is cal led a modified minimum norm solution (MMNS) method. Both the continuou s MMNS and its discretization are studied. The error estimates hold fo r some classes of band-limited signals, when the maximum magnitude of the data error is known. These classes of band-limited signals are als o characterized.