统计与随机过程在信号处理中的应用
出版时间:
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
-
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
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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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