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handout_week12_a

handout_week12_a - statistically independent • This...

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Stochastic Signals and Systems Random Processes Virginia Tech Fall 2008 Random Telegraph Signal Consider a random process X ( t ) that starts at the value X ( 0 ) = ± 1 with equal probability. At random times t 1 , t 2 , . . . thereafter it changes sign. The “switching times” t 1 , t 2 , . . . constitute a Poisson process with rate α ; that is, the number of changes of sign between any two times t 1 and t 2 has a Poisson distribution with rate α . the number of changes of sign in disjoint intervals are
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Unformatted text preview: statistically independent. • This process is called the random telegraph signal . Random Telegraph Signal P [ even number of sign changes in ( t 1 , t 2 )] = P [ odd number of sign changes in ( t 1 , t 2 )] = P [ X ( t ) = 1 ] = P [ X ( t ) =-1 ] = Random Telegraph Signal The mean, variance, and autocovariance of the random telegraph signal are m X ( t ) = Var ( X ( t )) = C X ( t 1 , t 2 ) =...
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