Abstract
This chapter extends the review of deterministic signals presented in Chap. 2 to cover sampling and Fourier analysis of stochastic signals. A brief summary of key concepts, such as continuous-time and sampled power spectral densities, is provided to establish notation and core concepts.
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Further background on stochastic processes can be found in
Åström KJ (1970) Introduction to stochastic control theory. Academic Press, New York
Brillinger DR (1974) Fourier analysis of stationary processes. Proc IEEE 62(12):1628–1643
Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, San Diego
Oppenheim AV, Schafer RW (1999) Discrete-time signal processing, 2nd edn. Prentice Hall, New York
Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes, 4th edn. McGraw-Hill, New York
Söderström T (2002) Discrete-time stochastic systems—estimation and control, 2nd. edn. Springer, London
The proof of a result closely related to the idea described in Remark 11.8 is given in
Feuer A, Goodwin GC (1996) Sampling in digital signal processing and control Birkhäuser, Boston, p 180 (Lemma 4.6.1)
Additional background on the use of the Hurwitz zeta function to derive Eq. (11.19) can be found in
Adamchik VS (2007) On the Hurwitz function for rational arguments. Appl Math Comput 187(1):3–12
Apostol TM (1976) Introduction to analytic number theory. Springer, Berlin
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Yuz, J.I., Goodwin, G.C. (2014). Background on Sampling of Stochastic Signals. In: Sampled-Data Models for Linear and Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-5562-1_11
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DOI: https://doi.org/10.1007/978-1-4471-5562-1_11
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5561-4
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