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.

In Section 7.3 we defined a random variable X as a function that maps each outcome of a probabilistic experiment to a real number. In a similar manner, a real-valued CT or DT random process, X(t) or X[n] respectively, is a function that maps each outcome of a probabilistic experiment to a real CT or DT signal respectively,

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