Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Behavior of Shannon's sampling series with applications
 Institute of Electrical and Electronics Engineers IEEE: IEEE International Symposium on Information Theory, ISIT 2007. Proceedings : 2429 June 2007, Nice, France Piscataway: IEEE Service Center, 2007 ISBN: 9781424413973 (print) ISBN: 9781424414291 ISBN: 1424413974 pp.301305 (Vol.1) 
 International Symposium on Information Theory (ISIT) <2007, Nice> 

 English 
 Conference Paper 
 Fraunhofer HHI () 
 interpolation; mathematical operator; series (mathematics); signal sampling 
Abstract
In this paper we discuss the interplay between discretetime and continuoustime signals and the question, whether certain properties of the signal in one domain carry over to the other domain. The Shannon sampling series and the more general Valiron interpolation series are the appropriate means to obtain the continuoustime, bandlimited signal out of its samples, i.e., the discretetime signal. Furthermore, we investigate the symmetric sampling series and the behavior of the nonsymmetric sampling series, which follows from the properties of the projection operator. It is well known, that the space of discretetime signals with finite energy and the space of continuous time, bandlimited signals with finite energy are isomorphic. Thus, discretetime and continuoustime, bandlimited signals with finite energy can be used interchangeably. This interchangeability is not restricted to finite energy signals. It is valid for a considerably larger class, but not for the space of bounded signals: Even if the discretetime signal is bounded, the corresponding bandlimited interpolation can be unbounded. For the proof we explicitly state such a bounded discretetime signal. Furthermore, we show not only that the Shannon sampling series diverges for this signal, but also that there is no bounded, bandlimited interpolation at all.