A NEW EXTRAPOLATION ALGORITHM FOR BAND-LIMITED SIGNALS USING THE REGULARIZATION METHOD

In this paper a new algorithm useful for band-limited extrapolation is presented. First, we consider the ill-posedness of the extrapolation problem in the face of noise. Then we construct a stable algorithm by solving a Fredholm equation based on a regularization method. The algorithm appears relatively robust since we have taken the noise eta(delta)(t) as a function in L2[-T, T] (T > 0) such that the error energy integral-T/-T\eta(delta)(t)\2 dt less-than-or-equal-to delta2 while the constructed extrapolation will uniformly converge to the desired signal over (-infinity, +infinity) as delta --> 0. We present an estimate for the error energy of the constructed extrapolation over (-infinity, +infinity) and also for the absolute error between the constructed extrapolation and the desired signal over (-infinity, +infinity).