Convergence behavior of non-equidistant sampling series |
| |
Authors: | Holger Boche,Ullrich J. M nich |
| |
Affiliation: | aTechnische Universität Berlin, Heinrich-Hertz-Chair for Mobile Communications, Einsteinufer 25, D-10587 Berlin, Germany |
| |
Abstract: | The convergence of sampling series with non-equidistant sampling points cannot be guaranteed for the Paley–Wiener space if the class of sampling patterns is not restricted. In this paper we consider sampling patterns that are made of the zeros of sine-type functions and analyze the local and global convergence behavior of the sampling series. It is shown that oversampling is necessary for global uniform convergence. If no oversampling is used there exists for every sampling pattern a signal such that the peak value of the approximation error grows arbitrarily large. Furthermore, we use the findings to derive results about the mean-square convergence behavior of the sampling series for bandlimited wide-sense stationary stochastic processes. Finally, a procedure is given to construct functions of sine type and possible sampling patterns. |
| |
Keywords: | Sampling series Sine type Non-equidistant sampling Reconstruction Stochastic process |
本文献已被 ScienceDirect 等数据库收录! |