On the extrapolation of band-limited functions with energy constraints

A modification of the algorithm proposed by Papoulis and Gerchberg for extrapolating band-limited functions is suggested to extend its applicability over data corrupted by noise. We assume that energy constraints are known either for the band-limited signal or for the noise. In addition, the discrete formulation of the iterative algorithm is derived, and the transition from the continuous algorithm to its digital implementation is presented.