introduction to statistical signal processing

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1、iAnIntroductiontoStatisticalSignalProcessingf−1(F)fFPr(f∈F)=P({ω:ω∈F})=P(f−1(F))-September10,2008iiAnIntroductiontoStatisticalSignalProcessingRobertM.GrayandLeeD.DavissonInformationSystemsLaboratoryDepartmentofElectricalEngineeringStanfordUniversityandDepartmentofElectricalEngi

2、neeringandComputerScienceUniversityofMarylandc2004byCambridgeUniversityPress.Copiesofthepdffilemaybedownloadedforindividualuse,butmultiplecopiescannotbemadeorprintedwithoutpermission.iiitoourFamiliesContentsPrefacepageixAcknowledgementsxiiGlossaryxiii1Introduction12Probability10

3、2.1Introduction102.2Spinningpointersandflippingcoins142.3Probabilityspaces222.4Discreteprobabilityspaces452.5Continuousprobabilityspaces542.6Independence692.7Elementaryconditionalprobability702.8Problems743Randomvariables,vectors,andprocesses833.1Introduction833.2Randomvariables

4、943.3Distributionsofrandomvariables1033.4Randomvectorsandrandomprocesses1133.5Distributionsofrandomvectors1163.6Independentrandomvariables1253.7Conditionaldistributions1283.8Statisticaldetectionandclassification1333.9Additivenoise1363.10BinarydetectioninGaussiannoise1433.11Stati

5、sticalestimation1453.12Characteristicfunctions1463.13Gaussianrandomvectors1523.14Simplerandomprocesses153vviContents3.15Directlygivenrandomprocesses1573.16DiscretetimeMarkovprocesses1593.17⋆Nonelementaryconditionalprobability1683.18Problems1694Expectationandaverages1834.1Averag

6、es1834.2Expectation1864.3Functionsofrandomvariables1894.4Functionsofseveralrandomvariables1964.5Propertiesofexpectation1964.6Examples1984.7Conditionalexpectation2074.8⋆JointlyGaussianvectors2104.9Expectationasestimation2124.10⋆Implicationsforlinearestimation2194.11Correlationan

7、dlinearestimation2224.12Correlationandcovariancefunctions2294.13⋆Thecentrallimittheorem2324.14Sampleaverages2354.15Convergenceofrandomvariables2374.16Weaklawoflargenumbers2444.17⋆Stronglawoflargenumbers2464.18Stationarity2514.19Asymptoticallyuncorrelatedprocesses2564.20Problems

8、2595Second-ordertheory2775.1Linearfilteringofrandomproc