Variance or spectral density in sampled data filtering?

Authors:
Graham C. Goodwin;Juan I. Yuz;Mario E. Salgado;Juan C. Agüero
Affiliations:
Centre for Complex Dynamic Systems and Control, The University of Newcastle, Newcastle, Australia;Department of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaiso, Chile;Department of Electronic Engineering, Universidad Técnica Federico Santa María, Valparaiso, Chile;Centre for Complex Dynamic Systems and Control, The University of Newcastle, Newcastle, Australia
Venue:
Journal of Global Optimization
Year:
2012

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Abstract

Most physical systems operate in continuous time. However, to interact with such systems one needs to take samples. This raises the question of the relationship between the sampled response and the response of the underlying continuous-time system. In this paper we review several aspects of the sampling process. In particular, we examine the role played by variance and spectral density in describing discrete random processes. We argue that spectral density has several advantages over variance. We illustrate the ideas by reference to the problem of state estimation using the discrete-time Kalman filter.