Stochastic processes are classes of signals whose fluctuations in time are partially or completely random. Examples of signals that can be modelled by a stochastic process are speech, music, image, time-varying channels, noise, and any information bearing function of time. Stochastic signals are completely described in terms of a probability model, but they can also be characterised with relatively simple statistics, such as the mean, the correlation and the power spectrum. This chapter begins with a study of the basic concepts of random signals and stochastic processes, and the models that are used for characterisation of random processes. We study the important concept of ergodic stationary processes in which time-averages obtained from a single realisation of a stochastic process can be used instead of the ensemble averages. We consider some useful and widely used classes of random signals, and study the effect of filtering or transformation of a signals on its probability distribution.


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  1. Anderson O.D. (1976), Time Series Analysis and Forecasting, The Box-Jenkins Approach, Butterworth, London.Google Scholar
  2. Ayre A.J. (1972), Probability and Evidence, Columbia University Press.Google Scholar
  3. Bartlett M.S. (1960), Stochastic Processes, Cambridge University Press, Cambridge.zbMATHGoogle Scholar
  4. Box G.E.P, Jenkins G.M. (1976), Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco.zbMATHGoogle Scholar
  5. Breiphol A.M. (1970), Probabilistic System Analysis, Wiley, New York.Google Scholar
  6. Carter G. (1987), Coherence and Time Delay Estimation, Proc. IEEE, Vol. 75, No. 2 Pages 236–55.CrossRefGoogle Scholar
  7. Chung K. L. (1974), Elementary Probability Theory, Springer-Verlag.zbMATHGoogle Scholar
  8. Clark A. B., Disney R. L. (1985), Probability and Random Processes, 2nd Ed. Wiley, New York.Google Scholar
  9. Cooper G. R., McGillem C.D. (1986), Probabilistic Methods of Signal and System Analysis Holt, Rinehart and Winston, New York.Google Scholar
  10. Davenport W.B., Root W. L. (1958), Introduction to Random Signals and Noise, McGraw-Hill, New York.zbMATHGoogle Scholar
  11. Davenport W.B., Wilbur B., (1970), Probability and Random Processes: An Introduction for Applied Scientists and Engineers., McGraw-Hill, New York.Google Scholar
  12. Einestein A. (1956) Investigation on the Theory of Brownian Motion, Dover, New York.Google Scholar
  13. Gauss K. G. (1963), Theory of Motion of Heavenly Bodies, Dover, New York.zbMATHGoogle Scholar
  14. Jeffrey H. (1961), Scientific Inference, 3rd ed. Cambridge University Press, Cambridge.Google Scholar
  15. Jeffrey H. (1973), Theory of Probability, 3rd ed. Clarendon Press, Oxford.Google Scholar
  16. Gardener W.A. (1986), Introduction to Random Processes: With Application to Signals and Systems, Macmillan, New York.Google Scholar
  17. Helstrom C.W. (1991), Probability and Stochastic Processes for Engineers, Macmillan, New York.Google Scholar
  18. Isaacson D., Masden R. (1976), Markov Chains Theory and Applications Wiley, New York.Google Scholar
  19. Kay S. M. (1993), Fundamentals of Statistical Signal Processing, Estimation Theory Prentice-Hall, Englewood Cliffs, N. J.zbMATHGoogle Scholar
  20. Kolmogorov A.N. (1956), Foundations of the Theory of Probability, Chelsea Publishing Company, New York.zbMATHGoogle Scholar
  21. Kendall M., Stuart A. (1977), The Advanced Theory of Statistics Macmillan.Google Scholar
  22. Leon-Garcia A. (1994), Probability and Random Processes for Electrical Engineering Addison Wesley, Reading, Mass.Google Scholar
  23. Markov A. A. (1913), An Example of Statistical Investigation in the text of Eugen Onyegin Illustrating Coupling of Tests in Chains, Proc. Acad. Sci. St Petersburg VI Ser., Vol. 7, Pages 153–162.Google Scholar
  24. Meyer P. L. (1970), Introductory Probability and Statistical Applications, Addison-Wesley, Reading, Mass.Google Scholar
  25. Peebles P.Z. (1987), Probability, Random Variables and Random Signal Principles McGraw-Hill, New York.Google Scholar
  26. Parzen E. (1962), Stochastic Processes, Holden-Day, San Francisco.zbMATHGoogle Scholar
  27. Populis A. (1984), Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York.Google Scholar
  28. Populis A. (1977), Signal Analysis, McGraw-Hill, New York.Google Scholar
  29. Rao C. R. (1973), Linear Statistical Inference and Its Applications, Wiley, New York.zbMATHCrossRefGoogle Scholar
  30. Rozanov Y. A. (1969), Probability Theory: A Concise Course, Dover Publications, New York.Google Scholar
  31. Shanmugan K. S., Breipohl A. M. (1988), Random Signals: Detection, Estimation and Data Analysis, Wiley, New York.Google Scholar
  32. Thomas J.B. (1988), An introduction to Applied probability and Random Processes, Huntington, Krieger Publishing, New York.Google Scholar
  33. Wozencraft J. M., Jacobs I. M. (1965), Principles of Communication Engineering, Wiley, New York.Google Scholar

Copyright information

© John Wiley & Sons Ltd. and B.G. Teubner 1996

Authors and Affiliations

  • Saeed V. Vaseghi
    • 1
  1. 1.Queen’s UniversityBelfastUK

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