On a conjecture of J.L.C. Sanz and T.S. Huang

In [1], Sanz and Huang conjectured that the DFT implementation of the Papoulis-Gerchberg algorithm for the extrapolation of band-limited signals does approach the continuous extrapolation. In this respect, we prove a result on the approximation of band-limited functions by trigonometric polynomials, simultaneously increasing their degree and the period length. This will imply that the above conjecture is indeed true.