On stable Shannon type reconstruction processes

In this paper symmetric and non-symmetric Shanon type sampling series that use samples taken at Nyquist rate are analyzed. It is shown that the symmetric series converges uniformly on the whole real axis, i.e., that it is a stable reconstruction process, for the Paley–Wiener space. This result is surprising, because recently it was shown that for a very general class of reconstruction processes a stable reconstruction is not possible for the Paley–Wiener space. However, there are some important differences. The analyzed Shannon type sampling series uses infinitely many samples for signal reconstruction and is not bandlimited. The characteristics stability, bandlimitedness, and the property of perfect reconstruction for a certain subspace are discussed. Furthermore, the corresponding non-symmetric series is analyzed. An explicit example shows that it is not stable.