Lecture15 - Basics Lecture 15 First recall an RV is a...

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•1 Lecture 15 Stochastic/Random Processes Basics First recall an RV is a mapping from which we denote by or When we add the notion of time to an RV to obtain we have a stochastic process. It is a rule for assigning to every a function R S R S X : ) ( ω X ) ( ξ X ) , ( t X S ). , ( t X It is a class of time functions depending on the parameter , or a function of t and of . If is a continuous time process. If or N, then is a discrete time process. A stochastic process may be viewed in any of the following ways: a) An ensemble of functions where are variables. b) A sample time function of a given process when is fixed. ) ( t X R t Z t ) ( t X ) , ( t X , t c) If t is fixed, and is variable, then it is a RV. d) If t and are fixed, X(t) is a number.
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•2 EXAMPLES Example: 1. The motion of particles(microscopic) in collision with other particles is one good instance of a stochastic process. 2. In communications, a received signal has a random amplitude and a random phase (In addition to random noise). )) ( cos( ) ( ) ( i i t A t X ξ ϕ ω + = Brownian Motion X(t) ± Characterization of stochastic processes: A stochastic process is basically a non- countably-infinite set of RV’s for each t.
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This note was uploaded on 09/24/2009 for the course ECE 514 taught by Professor Krim during the Fall '08 term at N.C. State.

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Lecture15 - Basics Lecture 15 First recall an RV is a...

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