A new extrapolation algorithm for band-limited signals using the regularization method

The ill-posedness of the extrapolation problem in the presence of noise is considered. A stable algorithm is constructed by solving a Fredholm equation based on a regularization method. The algorithm appears relatively robust, since the noise η_δ(t ) is taken as a function in L²[-T,T](T>0) such that the error energy ∫|η_δ(t)|² dt⩽δ², where integration is from - T to T, and the constructed extrapolation uniformly converges to the desired signal over (-∞, +∞) as δ→0. An estimate for the error energy of the constructed extrapolation over (-∞, +∞) and for the absolute error between the constructed extrapolation and the desired signal over (-∞, +∞) are presented