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1、CHAPTER9RandomProcessesINTRODUCTIONMuchofyourbackgroundinsignalsandsystemsisassumedtohavefocusedontheeffectofLTIsystemsondeterministicsignals,developingtoolsforanalyzingthisclassofsignalsandsystems,andusingwhatyoulearnedinordertounderstandapplicationsincommunication(e.g
2、.,AMandFMmodulation),control(e.g.,stabilityoffeedbacksystems),andsignalprocessing(e.g.,filtering).ItisimportanttodevelopacomparableunderstandingandassociatedtoolsfortreatingtheeffectofLTIsystemsonsignalsmodeledastheoutcomeofprobabilisticexperiments,i.e.,aclassofsignalsre
3、ferredtoasrandomsignals(alternativelyreferredtoasrandomprocessesorstochasticprocesses).Suchsignalsplayacentralroleinsignalandsystemdesignandanalysis,andthroughouttheremainderofthistext.Inthischapterwedefinerandomprocessesviatheassociatedensembleofsignals,andbegintoexplo
4、retheirproperties.Insuccessivechaptersweuserandomprocessesasmodelsforrandomoruncertainsignalsthatariseincommunication,controlandsignalprocessingapplications.9.1DEFINITIONANDEXAMPLESOFARANDOMPROCESSInSection7.3wedefinedarandomvariableXasafunctionthatmapseachoutcomeofapro
5、babilisticexperimenttoarealnumber.Inasimilarmanner,areal-valuedCTorDTrandomprocess,X(t)orX[n]respectively,isafunctionthatmapseachoutcomeofaprobabilisticexperimenttoarealCTorDTsignalrespectively,termedtherealizationoftherandomprocessinthatexperiment.Foranyfixedtimeinstan
6、tt=t0orn=n0,thequantitiesX(t0)andX[n0]arejustrandomvariables.Thecollectionofsignalsthatcanbeproducedbytherandomprocessisreferredtoastheensembleofsignalsintherandomprocess.EXAMPLE9.1RandomOscillatorsAsanexampleofarandomprocess,imagineawarehousecontainingNharmonicoscilla
7、tors,eachproducingasinusoidalwaveformofsomespecificamplitude,frequency,andphase,allofwhichmaybedifferentforthedifferentoscillators.Theprobabilisticexperimentthatresultsintheensembleofsignalsconsistsofselectinganoscillatoraccordingtosomeprobabilitymassfunction(PMF)thatassi
8、gnsaprobabilitytoeachofthenumbersfrom1toN,sothattheithoscillatorispicked°cAlanV.OppenheimandGeorgeC.Verghese,20101611
