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统计与随机过程在信号处理中的应用

统计与随机过程在信号处理中的应用
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作者: [美] （Stark H.） 著
出版社: 高等教育出版社
2008-01
版次: 1
ISBN: 9787040225822
定价: 57.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 719页
字数: 870千字
正文语种: 简体中文
丛书: 国外电气信息类优秀教材改编系列
分类: 工程技术
3 张插图图片
23人买过
  • 　　Thefirsteditioflofthisbook(1986)grewoutofasetofnotesusedbytheauthorstoteachtwoone-semestercoursesonprobabilityandrandomprocessesatRensse-laerPolytechnicInstitute(RPI).AtthattimetheprobabilitycourseatRPIwasre-quiredofallstudentsintheComputerandSystemsEngineeringProgramandwasahighlyrecommendedelectiveforstudentsincloselyrelatedareas.Whilemanyun-dergraduatestudentstookthecourseinthejunioryear,manyseniorsandfirst-yeargraduatestudentstookthecourseforcreditaswell.Then,asnow,mostofthestu-dentswereengineeringstudents.Toservethesestudentswell,wefeltthatweshouldberigorousinintroducingfundamentalprincipleswhilefurnishingmanyop-portunitiesforstudentstodeveloptheirskillsatsolvingproblems. IntroductiontoProbability
    1.1INTRODUCTION:WHYSTUDYPROBABILITY?
    1.2THEDIFFERENTKINDSOFPROBABILITY
    A.ProbabilityasIntuition
    B.ProbabilityastheRatioofFavorabletoTotalOutcomes（ClassicalTheory）
    C.ProbabilityasaMeasureofFrequencyofOccurrence
    D.ProbabilityBasedonanAxiomaticTheory
    1.3MISUSES,MISCALCULATIONS,ANDPARADOXES1N　PROBABILITY
    1.4SETS,FIELDS,ANDEVENTS　ExamplesofSampleSpaces
    1.5AXIOMATICDEFINITIONOFPROBABILITY
    1.6JOINT,CONDITIONAL,ANDTOTALPROBABILITIES;INDEPENDENCE
    1.7BAYESTHEOREMANDAPPLICATIONS
    1.8COMBINATORICS
    OccupancyProblems
    ExtensionsandApplications
    1.9BERNOULLITRIALS——BINOMIALANDMULTINOMIAL
    PROBABILITYLAWS
    MultinomialProbabilityLaw
    1.10ASYMPTOTICBEHAVIORoFTHEBINOMIALLAW：THEPOISSONLAW
    1.11NORMALAPPROXIMATIONTOTHEBINOMIALLAW
    1.12SUMMARY
    PROBLEMS
    REFERENCES

    2　RandomVariables
    2.1INTRODUCTION
    2.2DEFINITIONOFARANDOMVARIABLE
    2.3PROBABILITYDISTRIBUTIONFUNCTION
    2.4PROBABILITYDENSITYFUNCTION(pdf）FourOtherCommonDensityFunctionsMoreAdvancedDensityFunctions
    2.5CONTINUOUS,DISCRETE,ANDMIXEDRANDOMVARIABLES
    ExamplesofProbabilityMassFunctions
    2.6CONDITIONALANDJOINTDISTRIBUTIONSAND
    DENSITIES
    2.7FAILURERATES
    2.8FUNCTIONSOFARANDOMVARIABLE
    2.9SOLVINGPROBLEMSOFTHETYPE
    2.10SOLVINGPROBLEMSOFTHETYPE
    2.11SOLVINGPROBLEMSOFTHETYPEW=h(X,Y）
    2.12SUMMARY
    PROBLEMS
    REFERENCES
    ADDITIONALREADING

    3.ExpectationandIntroductiontoEstimation
    3.1EXPECTEDVALUEOFARANDOMVARIABLEOntheValidityofEquation3.1-8
    3.2CONDITIONALEXPECTATIONS
    ConditionalExpectationasaRandomVariable
    3.3MOMENTS
    JointMoments
    PropertiesofUncorrelatedRandomVariables
    JointlyGaussianRandomVariables
    ContoursofConstantDensityoftheJointGaussianpd{
    3.4CHEBYSHEVANDSCHWARZINEQUALITIES
    RandomVariableswithNonnegativeValues
    TheSchwarzInequality
    3.5MOMENT-GENERATINGFUNCTIONS
    3.6CHERNOFFBOUND
    3.7CHARACTERISTICFUNCTIONS
    JointCharacteristicFunctions
    TheCentralLimitTheorem
    3.8ESTIMATORSFORTHEMEANANDVARIANCEOFTHE
    NORMALLAW
    ConfidenceIntervals{ortheMean
    ConfidenceIntervalfortheVariance
    3.9SUMMARY
    PROBLEMS
    REFERENCES
    ADDITIONALREADING

    4RandomVectorsandParameterEstimation
    4.1JOINTDISTRIBUTIONANDDENSITIES
    4.2EXPECTATIONVECTORSANDCOVARIANCEMATRICES
    4.3PROPERTIESOFCOVARIANCEMATRICES
    4.4SIMULTANEOUSDIAGONALIZATIONOFTWO
    COVARIANCEMATRICESANDAPPLICATIONSIN
    PATTERNRECOGNITION
    Projection
    MaximizationofQuadraticForms
    4.5THEMULTIDIMENSIONALGAUSSIAN(NORMAL）LAW
    4.6CHARACTERISTICFUNCTIONSOFRANDOMVECTORS
    TheCharacteristicFunctionoftheGaussian(Normal）Law
    4.7PARAMETERESTIMATION
    EstimationofE[X]
    4.8ESTIMATIONOFVECTORMEANSANDCOVARIANCE
    MATRICES
    Estimationof
    EstimationoftheCovarianceK
    4.9MAXIMUMLIKELIHOODESTIMATORS
    4.10LINEARESTIMATIONOFVECTORPARAMETERS
    4.11SUMMARY
    PROBLEMS
    REFERENCES
    ADDITIONALREADING

    5RandomSequences
    5.1BASICCONCEPTS
    Infinite-LengthBernoulliTrials
    ContinuityofProbabilityMeasure
    StatisticalSpecificationofaRandomSequence
    5.2BASICPRINCIPLESOFDISCRETE-TIMELINEARSYSTEMS
    5.3RANDOMSEQUENCESANDLINEARSYSTEMS
    5.4WSSRANDOMSEQUENCES
    PowerSpectralDensity
    InterpretationofthePSD
    SynthesisofRandomSequencesandDiscrete-TimeSimulation
    Decimation
    Interpolation
    5.5MARKOVRANDOMSEQUENCES
    ARMAModels
    MarkovChains
    5.6VECTORRANDOMSEQUENCESANDSTATEEQUATIONS
    5.7CONVERGENCEOFRANDOMSEQUENCES
    5.8LAWSOFLARGENUMBERS
    5.9SUMMARY
    PROBLEMS
    REFERENCES

    6Randomprocesses
    7AdvancedTopicsinRandomProcesses
    8ApplicationstoStatisticalSignalProcessing
  • 内容简介:
    　　Thefirsteditioflofthisbook(1986)grewoutofasetofnotesusedbytheauthorstoteachtwoone-semestercoursesonprobabilityandrandomprocessesatRensse-laerPolytechnicInstitute(RPI).AtthattimetheprobabilitycourseatRPIwasre-quiredofallstudentsintheComputerandSystemsEngineeringProgramandwasahighlyrecommendedelectiveforstudentsincloselyrelatedareas.Whilemanyun-dergraduatestudentstookthecourseinthejunioryear,manyseniorsandfirst-yeargraduatestudentstookthecourseforcreditaswell.Then,asnow,mostofthestu-dentswereengineeringstudents.Toservethesestudentswell,wefeltthatweshouldberigorousinintroducingfundamentalprincipleswhilefurnishingmanyop-portunitiesforstudentstodeveloptheirskillsatsolvingproblems.
  • 目录:
    IntroductiontoProbability
    1.1INTRODUCTION:WHYSTUDYPROBABILITY?
    1.2THEDIFFERENTKINDSOFPROBABILITY
    A.ProbabilityasIntuition
    B.ProbabilityastheRatioofFavorabletoTotalOutcomes（ClassicalTheory）
    C.ProbabilityasaMeasureofFrequencyofOccurrence
    D.ProbabilityBasedonanAxiomaticTheory
    1.3MISUSES,MISCALCULATIONS,ANDPARADOXES1N　PROBABILITY
    1.4SETS,FIELDS,ANDEVENTS　ExamplesofSampleSpaces
    1.5AXIOMATICDEFINITIONOFPROBABILITY
    1.6JOINT,CONDITIONAL,ANDTOTALPROBABILITIES;INDEPENDENCE
    1.7BAYESTHEOREMANDAPPLICATIONS
    1.8COMBINATORICS
    OccupancyProblems
    ExtensionsandApplications
    1.9BERNOULLITRIALS——BINOMIALANDMULTINOMIAL
    PROBABILITYLAWS
    MultinomialProbabilityLaw
    1.10ASYMPTOTICBEHAVIORoFTHEBINOMIALLAW：THEPOISSONLAW
    1.11NORMALAPPROXIMATIONTOTHEBINOMIALLAW
    1.12SUMMARY
    PROBLEMS
    REFERENCES

    2　RandomVariables
    2.1INTRODUCTION
    2.2DEFINITIONOFARANDOMVARIABLE
    2.3PROBABILITYDISTRIBUTIONFUNCTION
    2.4PROBABILITYDENSITYFUNCTION(pdf）FourOtherCommonDensityFunctionsMoreAdvancedDensityFunctions
    2.5CONTINUOUS,DISCRETE,ANDMIXEDRANDOMVARIABLES
    ExamplesofProbabilityMassFunctions
    2.6CONDITIONALANDJOINTDISTRIBUTIONSAND
    DENSITIES
    2.7FAILURERATES
    2.8FUNCTIONSOFARANDOMVARIABLE
    2.9SOLVINGPROBLEMSOFTHETYPE
    2.10SOLVINGPROBLEMSOFTHETYPE
    2.11SOLVINGPROBLEMSOFTHETYPEW=h(X,Y）
    2.12SUMMARY
    PROBLEMS
    REFERENCES
    ADDITIONALREADING

    3.ExpectationandIntroductiontoEstimation
    3.1EXPECTEDVALUEOFARANDOMVARIABLEOntheValidityofEquation3.1-8
    3.2CONDITIONALEXPECTATIONS
    ConditionalExpectationasaRandomVariable
    3.3MOMENTS
    JointMoments
    PropertiesofUncorrelatedRandomVariables
    JointlyGaussianRandomVariables
    ContoursofConstantDensityoftheJointGaussianpd{
    3.4CHEBYSHEVANDSCHWARZINEQUALITIES
    RandomVariableswithNonnegativeValues
    TheSchwarzInequality
    3.5MOMENT-GENERATINGFUNCTIONS
    3.6CHERNOFFBOUND
    3.7CHARACTERISTICFUNCTIONS
    JointCharacteristicFunctions
    TheCentralLimitTheorem
    3.8ESTIMATORSFORTHEMEANANDVARIANCEOFTHE
    NORMALLAW
    ConfidenceIntervals{ortheMean
    ConfidenceIntervalfortheVariance
    3.9SUMMARY
    PROBLEMS
    REFERENCES
    ADDITIONALREADING

    4RandomVectorsandParameterEstimation
    4.1JOINTDISTRIBUTIONANDDENSITIES
    4.2EXPECTATIONVECTORSANDCOVARIANCEMATRICES
    4.3PROPERTIESOFCOVARIANCEMATRICES
    4.4SIMULTANEOUSDIAGONALIZATIONOFTWO
    COVARIANCEMATRICESANDAPPLICATIONSIN
    PATTERNRECOGNITION
    Projection
    MaximizationofQuadraticForms
    4.5THEMULTIDIMENSIONALGAUSSIAN(NORMAL）LAW
    4.6CHARACTERISTICFUNCTIONSOFRANDOMVECTORS
    TheCharacteristicFunctionoftheGaussian(Normal）Law
    4.7PARAMETERESTIMATION
    EstimationofE[X]
    4.8ESTIMATIONOFVECTORMEANSANDCOVARIANCE
    MATRICES
    Estimationof
    EstimationoftheCovarianceK
    4.9MAXIMUMLIKELIHOODESTIMATORS
    4.10LINEARESTIMATIONOFVECTORPARAMETERS
    4.11SUMMARY
    PROBLEMS
    REFERENCES
    ADDITIONALREADING

    5RandomSequences
    5.1BASICCONCEPTS
    Infinite-LengthBernoulliTrials
    ContinuityofProbabilityMeasure
    StatisticalSpecificationofaRandomSequence
    5.2BASICPRINCIPLESOFDISCRETE-TIMELINEARSYSTEMS
    5.3RANDOMSEQUENCESANDLINEARSYSTEMS
    5.4WSSRANDOMSEQUENCES
    PowerSpectralDensity
    InterpretationofthePSD
    SynthesisofRandomSequencesandDiscrete-TimeSimulation
    Decimation
    Interpolation
    5.5MARKOVRANDOMSEQUENCES
    ARMAModels
    MarkovChains
    5.6VECTORRANDOMSEQUENCESANDSTATEEQUATIONS
    5.7CONVERGENCEOFRANDOMSEQUENCES
    5.8LAWSOFLARGENUMBERS
    5.9SUMMARY
    PROBLEMS
    REFERENCES

    6Randomprocesses
    7AdvancedTopicsinRandomProcesses
    8ApplicationstoStatisticalSignalProcessing
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