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Unformatted text preview: Stochastic Signals and Systems Random Processes Virginia Tech Fall 2008 Mean and Correlation Functions • As in the case of rvs, the moment functions play an important role in practical applications. These functions, however, only partially describe a random process. • The mean function m X ( t ) of a random process X ( t ) is defined by m X ( t ) = E [ X ( t )] = Z ∞-∞ xf X ( t ) ( x ) dx , where f X ( t ) ( x ) is the pdf of X ( t ) . In general, m X ( t ) is a function of time. • The variance function of X ( t ) is defined by σ 2 X ( t ) = E h ( X ( t )- m X ( t )) 2 i = Z ∞-∞ ( x- m X ( t )) 2 f X ( t ) ( x ) dx Mean and Correlation Functions • The autocorrelation function R X ( t 1 , t 2 ) of a random process X ( t ) is defined as R X ( t 1 , t 2 ) = E [ X ( t 1 ) X ( t 2 )] = Z ∞-∞ Z ∞-∞ xyf X ( t 1 ) , X ( t 2 ) ( x , y ) dxdy , where f X ( t 1 ) , X ( t 2 ) ( x , y ) is the second order pdf of X ( t ) ....
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This note was uploaded on 05/05/2010 for the course ECECS 5605 taught by Professor Dasilver during the Fall '08 term at Virginia Tech.
- Fall '08