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Analytic Properties of Random Processes

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Properties  ::  Continuity  ::  Differentiation  ::  Integration

Analytic Properties of Random Processes

Let $X_t$ be a function of time, and let $h(t)$ be the impulse response of a (continuous-time) linear time invariant system. If $X_t$ is the input to the system, then the output is

\begin{displaymath}Y_t = X_t * h(t) = \int_{-\infty}^\infty h(t-\tau) X_\tau d\tau.
\end{displaymath}

We will consider such operations when $X_t$ is a random process. This will require us to develop some additional analytic properties of random processes.
Copyright 2008, Todd Moon. Cite/attribute Resource . admin. (2006, June 07). Analytic Properties of Random Processes. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Stochastic_Processes/lecture7_1.htm. This work is licensed under a Creative Commons License Creative Commons License