Signals, Systems and Inference, Chapter 9: Random Processes

C H A P T E R 9 Random Processes INTRODUCTION Much of your background in signals and Systems is assumed to have focused on the effect of LTI Systems on deterministic signals, developing tools for analyzing this class of signals and Systems , and using what you learned in order to understand applications in communication ( , AM and FM modulation), control ( , sta bility of feedback Systems ), and signal processing ( , filtering). It is important to develop a comparable understanding and associated tools for treating the effect of LTI Systems on signals modeled as the outcome of probabilistic experiments, , a class of signals referred to as Random signals (alternatively referred to as Random Processes or stochastic Processes ). Such signals play a central role in signal and system design and analysis, and throughout the remainder of this text.

FIGURE 9.2 Real izat ons of the random process X(t) can be thought of as a family of jointly distributed random variables indexed by t (or n in the DT case). A full probabilistic characterization of this collection of random variables would require the joint PDFs of multiple samples of the signal, taken at arbitrary times: a X(t) = x (t)b

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