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Unformatted text preview: a 1 , a 2 , . . . , a N , N X k = 1 N X l = 1 a k a * l R X ( t kt l ) ≥ • The autocorrelation function is a measure of the rate of change of a random process P [  X ( t + τ )X ( t )  > ± ] = 2 { R X ( )R X ( τ ) } ± 2 Properties Autocorrelation Func. Stationary Processes • A WSS random process X ( t ) is meansquare periodic if for some T we have R X ( τ ) = R X ( τ + T ) for all τ . We call the smallest such T > 0 the period . Note: If a WSS random process X ( t ) is m.s. periodic, then its power spectral density is a line spectra with impulses at multiples of the fundamental frequency ω = 2 π/ T . • The autocorrelation function can have three types of components: (1) A component that approaches zero as τ → ∞ ; (2) A periodic component; and (3) A component due to a nonzero mean....
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 Fall '08
 DASILVER
 Stochastic process, Autocorrelation, Stationary process, covariance function, Properties Autocorrelation Func

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