There Exists No Globally Uniformly Convergent Reconstruction for the Paley–Wiener Space ${{cal PW}}_{pi}^{1}$ of Bandlimited Functions Sampled at Nyquist Rate

摘要

The bandlimited interpolation of signals and the convergence behavior of the Shannon sampling series are discussed in order to show that it is desirable to have a uniformly convergent reconstruction, for as large a space of signals as possible.