an introduction to statistical signal processing

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1、AnIntroductiontoStatisticalSignalProcessingf−1(F)fFPr(f∈F)=P({ω:ω∈F})=P(f−1(F))✲May5,2000iiAnIntroductiontoStatisticalSignalProcessingRobertM.GrayandLeeD.DavissonInformationSystemsLaboratoryDepartmentofElectricalEngineeringStanfordUniversityandDepartmentofElectricalEngineeringand

2、ComputerScienceUniversityofMarylandivc1999bytheauthors.vtoourFamiliesviContentsPrefacexiGlossaryxv1Introduction12Probability112.1Introduction...........................112.2SpinningPointersandFlippingCoins............152.3ProbabilitySpaces.......................232.3.1SampleSpac

3、es.....................282.3.2EventSpaces......................312.3.3ProbabilityMeasures..................422.4DiscreteProbabilitySpaces..................452.5ContinuousProbabilitySpaces................562.6Independence..........................702.7ElementaryConditionalProbabil

4、ity.............712.8Problems............................753RandomObjects853.1Introduction...........................853.1.1RandomVariables...................853.1.2RandomVectors....................893.1.3RandomProcesses...................933.2RandomVariables.....................

5、..953.3DistributionsofRandomVariables..............1043.3.1Distributions......................1043.3.2MixtureDistributions.................1083.3.3DerivedDistributions.................1113.4RandomVectorsandRandomProcesses...........1153.5DistributionsofRandomVectors..............

6、.117viiviiiCONTENTS3.5.1MultidimensionalEvents...............1183.5.2MultidimensionalProbabilityFunctions.......1193.5.3ConsistencyofJointandMarginalDistributions..1203.6IndependentRandomVariables................1273.6.1IIDRandomVectors..................1283.7ConditionalDistribu

7、tions...................1293.7.1DiscreteConditionalDistributions..........1303.7.2ContinuousConditionalDistributions........1313.8StatisticalDetectionandClassification............1343.9AdditiveNoise.........................1373.10BinaryDetectioninGaussianNoise.............1443.11S

8、tatisticalEstimation....................