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4 - Overview of Mathematical Tools

from Part I - Fundamentals

Published online by Cambridge University Press:  23 December 2021

Marco Tartagni
Marco Tartagni
Affiliation:
University of Bologna
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Summary

This chapter gives a short summary of mathematical instruments required to model sensor systems in the presence of both deterministic and random processes. The concepts are organized in a compact overview for a more rapid consultation, emphasizing the convergences between different contexts.

Keywords

random signalsrandom processescorrelationautocorrelationLorentzianCarson theoremCampbell theoremergodicityrandom walkWiener-Kinchin theoremnoise equivalent bandwidthnoise correlation coefficientpower spectral densitycross power spectral density
Type
Chapter
Information
Electronic Sensor Design Principles , pp. 189 - 235
Publisher: Cambridge University Press
Print publication year: 2022

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References

Further Reading

Carlson, A. B., Communication Systems: An Introduction to Signal and Noise in Electrical Communication. New York: McGraw-Hill, 1986.Google Scholar
Gardner, W. A., An Introduction to Random Processes with Application to Signal and Systems. New York: McGraw-Hill, 1990.Google Scholar
Oppenheim, A. V., and Schafer, R. W., Discrete-Time Signal Processing. Upper Saddle River, NJ: Pearson Education, 2011.Google Scholar
Oppenheim, A. V., and Willsky, A. S., Signals and Systems. Upper Saddle River, NJ: Pearson Education, 2013.Google Scholar
Papoulis, A., and Pillai, S. U., Probability, Random Variables, and Stochastic Processes. New York: McGraw-Hill, 2002.Google Scholar
Proakis, J. G., and Manolakis, D. G., Digital Signal Processing. Upper Saddle River, NJ: Pearson Prentice Hall, 2007.Google Scholar

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