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Stationary Signals

In: A First Course in Statistics for Signal Analysis

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  • Wojbor A. Woyczyński

    (Case Western Reserve University, Department of Statistics and Center for Stochastic and Chaotic Processes in Sciences and Technology)

Abstract

In this chapter we introduce basic concepts necessary to study the time-dependent dynamics of random phenomena. The latter will be modeled as a family of random quantities indexed by a parameter, interpreted in this book as time. The parameter may be either continuous or discrete. Depending on the context, and on the tradition followed by different authors, such families are called random signals, stochastic processes, or (random) time series. The emphasis here is on random dynamics that are stationary, that is, governed by underlying statistical mechanisms that do not change in time, although, of course, particular realizations of such families will be functions that vary with time. Think here about a random signal produced by the proverbial repeated coin tossing; the outcomes vary while the fundamental mechanics remain the same.

Suggested Citation

  • Wojbor A. Woyczyński, 2011. "Stationary Signals," Springer Books, in: A First Course in Statistics for Signal Analysis, chapter 0, pages 105-125, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-8101-2_4
    DOI: 10.1007/978-0-8176-8101-2_4
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