THE CONVERGENCE BEHAVIOR OF AN ALGORITHM FOR THE RECONSTRUCTION OF BAND-LIMITED SIGNALS AND THEIR HILBERT TRANSFORM

Holger Boche - Marcus Protzmann

   Concerning the algorithm proposed by Papoulis and Gerchberg (see [13]) which allows the approximation of band-limited signals or its inverse version, in this paper statements shall be 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 so of the analytic signal without additional expense, too. Finally, the type and rate of convergence of the algorithm will be demonstrated by a numerical example.

Keywords: band-limited functions, continuous reconstruction, convergence properties, Fourier transform, Hilbert transform.

[full-paper]