an introduction to random optimum

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1、AnIntroductiontoRandom,OptimumandAdaptiveSignalProcessingDougGrayCSSIPContentsNotation3Chapter1.Preliminaries41.1.Introduction41.2.PrinciplesofOptimisationandAdaption41.3.TheCharacteristicsofAdaptiveSystems51.4.OptimumandAdaptiveSystemStructures61.5.DetailedStructuresforGe

2、nericApplications71.6.SystemIssues111.7.RepresentationofLinearSystems—discretetimelinearfilter121.8.Filtertransferfunction12Chapter2.TheoryofRandomProcesses1142.1.ProbabilityDensityFunctions142.2.StationaryRandomProcesses162.3.EnsembleAveraging182.4.Ergodicity202.5.Covarian

3、ces212.6.GaussianRandomProcess232.7.UncorrelatedRandomProcesses232.8.CovarianceMatricesandtappeddelaylines242.9.CovarianceMatrixEstimation262.10.MeanOutputPower272.11.Z-transformofaStationaryRandomProcess282.12.ConventionalSpectrumEstimation302.13.StatisticalPropertiesofS^

4、Ns(f)30Chapter3.OptimumDiscreteTimeLinearFiltering333.1.MeanSquareError(MSE)Surface333.2.MinimizingtheMSE353.3.Examples363.4.PrincipleofOrthogonality373.5.Extensiontocomplexcase38Stepsforderivingtheoptimalfilter403.6.CanonicalFormoftheErrorSurface413.7.FrequencyDomainFormul

5、ationofOptimumWienerFilters43Appendix:AlternativeDerivations45Chapter4.ConstrainedOptimisationandSpectrumAnalysis474.1.ConstrainedOptimumFilters474.2.ApplicationtoSpectrumAnalysis484.3.SampleMatrixInversionforConstrainedSpectralEstimation521CONTENTS2Chapter5.GradientDescen

6、tandLMSAlgorithms535.1.GradientSearch—Oneweightexample535.2.MultiweightCase555.3.Convergenceandcanonicalform575.4.Rapproachmentwithweightvector-eigenvaluespread585.5.ConvergenceDiscussion595.6.LMSAlgorithm(WidrowandHoff1960)605.7.NotesregardingLMSAlgorithm615.8.Convergence

7、625.9.Outputerrorbehaviour65Chapter6.LeastSquaresandRecursiveLeastSquares696.1.Reformulationoflinearfilteringasalinearleastsquaresestimationproblem.696.2.Principleoforthogonality706.3.Normalequations726.4.Minimumerror746.5.ProjectionOperatorInterpretation756.6.Propertiesoft

8、heLSestimate(General)756.7.WeightedLeastSquares766.8.RecursiveLeastSquares(RLS)776.9.RLSw