The convergence behavior of an algorithm for the reconstruction of band-limited signals and their Hilbert transform

By considering the algorithm proposed by Papoulis and Gerchberg (1962) which allows the approximation of bandlimited signals or its inverse version, statements are proven about the type and rate of convergence. These statements show that the convergence properties of the algorithm are very poor. Additionally, a modification of the algorithm is proposed which permits the approximation of the Hilbert transform of the signal and of the analytic signal without additional expense, too. Finally, the type and rate of convergence of the algorithm is demonstrated by a numerical example