Sampling and linear algebra

R. Moddemeijer

University of Groningen, Department of Computing Science,
P.O. Box 800, NL-9700 AV Groningen, The Netherlands,
phone: +31.50.363 3940 - fax: +31.50.363 38005 - e-mail: rudy@cs.rug.nl

Abstract

Shannon, in his landmark publication, mentions the geometric representation of continuous time signals. In more recent literature linear algebra is hardly used to interpret the sampling of signals. We show thant sampling and the reconstruction of signals with a minimum mean square error corresponds with the computation of inner products of basis functions with a time-signal, an orthogonalisation and the reconstruction by a coefficient weighted sum of basis functions. The reconstruction error is caused by the projection of the signal onto a space determined by the basis functions. Shannon's sampling theorem corresponds with a special case determined by the basis functions which are shifted in time. Sampling, orthogonalisation and reconstruction can be done by (digital) linear filtering. These filters can be chosen causal, but they can not be all FIR-filters. The interpretation of sampling using linear algebra leads to alternative sampling procedures.

Published

Eleventh Symposium on Information Theory in the Benelux, October 25-26, 1990, Noorwijkerhout, The Netherlands, Ed. Lubbe, J.C.A. van der, pp. 118-125, Werkgemeenschap Informatie- en Communicatietheorie, Enschede, and IEEE Benelux Chapter on Information Theory, ISBN 90-71048-06-3, BibTeX
other publications