Measuring Process via Sampling of Signals, and Functions with Attributes

Authors

Abstract

In this paper, it has been shown that any measuring process can be modeled as a process of sampling of signals.  Also, a notion of a special kind of functions, called here functions with attributes, has been introduced. The starting point here, in the first of the above themes, is an observation that in fact we are not able to measure and record truly continuously in time any physical quantity. The measuring process can be viewed as going stepwise that is in steps from one instant to another, similarly as a sampling of signals proceeds. Therefore, it can be modeled as the latter one. We discuss this in more detail here. And, the notion of functions with attributes, we introduced here, follows in a natural way from the interpretation of both the measuring process as well as the sampling of signals that we present in this paper. It turns out to be useful.

References

A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, New York: John Wiley & Sons, 2011.

R. J. Marks II, Introduction to Shannon Sampling and Interpolation Theory, New York: Springer-Verlag, 1991.

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, New York: Pearson, 2010.

W. E. Sabin, Discrete-Signal Analysis and Design, New York: John Wiley & Sons, 2008.

K. Sozański, Digital Signal Processing in Power Electronics Control Circuits, London: Springer-Verlag, 2013.

U. Zölzer, Digital Audio Signal Processing, Chichester: John Wiley & Sons, 2008.

A. Papoulis, “Generalized sampling expansion”, IEEE Trans. Circuits and Systems, vol. 24, pp. 652-654, Nov. 1977.

F. Marvasti, M. Analoui, and M. Gamshadzahi, “Recovery of signals from nonuniform samples using iterative methods”, IEEE Trans. Signal Proc., vol. 39, pp. 872-877, April 1991.

E.V.D. Ouderra and J. Renneboog, “Some formulas and applications of nonuniform sampling of bandwidth limited signals”, IEEE Trans. on Instrum. and Measurement, vol. 37, pp. 353-357, Sept. 1988.

P.P. Vaidyanathan, “Generalizations of the sampling theorem: seven decades after Nyquist”, IEEE Trans. on Circuits and Systems-I Fundamental Theory and Applications, vol. 48, pp. 1094-1109, Sept. 2001.

H. J. Landau, “Necessary density conditions for sampling and interpolation of certain entire functions”, Acta Math., vol. 117, pp. 37–52, 1967.

F. Marvasti (Ed.), Nonuniform Sampling: Theory and Practice, New York: Springer-Verlag, 2001.

K. Kuratowski, Introduction To Set Theory and Topology, Oxford, United Kingdom: Pergamon Press, 1961.

Available at: http://mathworld.wolfram.com/DirichletFunction.html, Dirichlet function, Oct. 2019.

Available at: https://en.wikipedia.org/wiki/Nowhere continuous function, Oct. 2019.

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Published

2024-04-19

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Section

Signals, Circuits, Systems