Background on Sampling of Stochastic Signals

  • Juan I. Yuz
  • Graham C. Goodwin
Part of the Communications and Control Engineering book series (CCE)


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.


Power Spectral Density Noise Sequence Deterministic Signal Stochastic Signal Continuous Sample Path 
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Further Reading

Further background on stochastic processes can be found in

  1. Åström KJ (1970) Introduction to stochastic control theory. Academic Press, New York zbMATHGoogle Scholar
  2. Brillinger DR (1974) Fourier analysis of stationary processes. Proc IEEE 62(12):1628–1643 MathSciNetCrossRefGoogle Scholar
  3. Jazwinski AH (1970) Stochastic processes and filtering theory. Academic Press, San Diego zbMATHGoogle Scholar
  4. Oppenheim AV, Schafer RW (1999) Discrete-time signal processing, 2nd edn. Prentice Hall, New York Google Scholar
  5. Papoulis A, Pillai SU (2002) Probability, random variables, and stochastic processes, 4th edn. McGraw-Hill, New York Google Scholar
  6. Söderström T (2002) Discrete-time stochastic systems—estimation and control, 2nd. edn. Springer, London CrossRefzbMATHGoogle Scholar

The proof of a result closely related to the idea described in Remark 11.8 is given in

  1. Feuer A, Goodwin GC (1996) Sampling in digital signal processing and control Birkhäuser, Boston, p 180 (Lemma 4.6.1) CrossRefzbMATHGoogle Scholar

Additional background on the use of the Hurwitz zeta function to derive Eq. (11.19) can be found in

  1. Adamchik VS (2007) On the Hurwitz function for rational arguments. Appl Math Comput 187(1):3–12 MathSciNetCrossRefzbMATHGoogle Scholar
  2. Apostol TM (1976) Introduction to analytic number theory. Springer, Berlin CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Juan I. Yuz
    • 1
  • Graham C. Goodwin
    • 2
  1. 1.Departamento de ElectrónicaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.School of Electrical Engineering & Computer ScienceUniversity of NewcastleCallaghanAustralia

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