handout_week12_b

handout_week12_b - Stochastic Signals and Systems Random...

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Unformatted text preview: Stochastic Signals and Systems Random Processes Virginia Tech Fall 2008 Stationary Random Processes We say a random process is stationary when its statistics do not change with time. • An observation of the process in the time interval ( t , t 1 ) exhibits the same type of random behavior as an observation in some other time interval ( t + τ, t 1 + τ ) . Stationary Random Processes A discrete-time or continuous-time random process X ( t ) is stationary if the joint distribution of any set of samples does not depend on the placement of the time origin: F X ( t 1 ) ,..., X ( t k ) ( x 1 , .. . , x k ) = F X ( t 1 + τ ) ,..., X ( t k + τ ) ( x 1 , .. . , x k ) for all time shifts τ , all k , and all choices of time samples t 1 , .. . , t k . • The first-order cdf of a stationary random process must be independent of time, since F X ( t ) ( x ) = F X ( t + τ ) ( x ) = F X ( x ) all t , τ....
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handout_week12_b - Stochastic Signals and Systems Random...

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