There Exists No Globally Uniformly Convergent Reconstruction for the Paley–Wiener Space of Bandlimited Functions Sampled at Nyquist Rate

Authors:
H. Boche;U.J. Monich
Affiliations:
Heinrich Hertz Chair for Mobile Commun., Tech. Univ. of Berlin, Berlin;-
Venue:
IEEE Transactions on Signal Processing - Part II
Year:
2008

Citing 0
Cited 5

Convergence behavior of non-equidistant sampling series

Signal Processing
An impossibility result for linear signal processing under thresholding

IEEE Transactions on Signal Processing
Unboundedness of thresholding and quantization for bandlimited signals

Signal Processing
On the hilbert transform of bounded bandlimited signals

Problems of Information Transmission
Uniqueness and reconstruction theorems for pseudodifferential operators with a bandlimited Kohn-Nirenberg symbol

Advances in Computational Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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. In this paper general sampling series are analyzed for the frequently utilized Paley-Wiener space PW pi 1, which is the largest space in the scale of Paley-Wiener spaces. The analysis is done not only for the Shannon sampling series, but for a whole class of axiomatically defined reconstruction processes. It is shown that for this very general class, which contains all common sampling series including the Shannon sampling series, a uniformly convergent reconstruction is not possible for the space PW pi 1. Moreover, a universal signal is identified that causes the divergence behavior for all sampling series. Finally, a lower and an upper bound are derived and used to describe the asymptotic behavior of the peak value of the finite sampling series.