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Topic 7: Random Processes

Topic7: RandomProcesses De nition,discreteandcontinuousprocesses Specifyingrandomprocesses{ joint cdf's or pdf's{Mean,auto-covariance,auto-correlat ion{Cross-covariance,cross-correlation StationaryprocessesandergodicityES150{ Harvard SEAS1 Randomprocesses Arandomprocess, alsocalledastochasticprocess, is a familyof randomvariables,indexedby a parametertfromanindexingsetT. For eachexperiment outcome!2 ,we assigna functionXthatdependsontX(t; !)t2T; !2 {tis typicallytime,butcanalsobe a spatialdimension{tcanbe discreteor continuous{Therangeoftcanbe nite,butmoreoftenis in nite,which meanstheprocesscontainsanin nitenumber of randomvariables.}}}}}}}

ES150 { Harvard SEAS 4. ... † Their joint behavior is completely specifled by the joint distributions for all combinations of their time samples. ... Xn = §1 with probability 1 2 for n even Xn = ¡1=3 and 3 with probabilities 9 10 and 1 10 for n odd † Properties of a WSS process:

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Topic 6: Convergence and Limit Theorems

www.ece.tufts.edu

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White noise † Band-limited white noise: A zero-mean WSS process N(t) which has the psd as a constant N0 2 within ¡W • f • W and zero elsewhere. { Similar to white light containing all frequencies in equal amounts.

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