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
) 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.