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Sampling and linear algebra

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

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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.

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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,
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