Xian-Da Zhang Modern Signal Processing De Gruyter STEM Also of interest 5G An Introduction to the 5th Generation Mobile Networks Ulrich Trick, 2021 ISBN 978-3-11-072437-0, e-ISBN (PDF) 978-3-11-072450-9, e-ISBN (EPUB) 978-3-11-072462-2 Digital Electronic Circuits Principles and Practices Shuqin Lou, Chunling Yang, 2019 ISBN 978-3-11-061466-4, e-ISBN (PDF) 978-3-11-061491-6, e-ISBN (EPUB) 978-3-11-061493-0 Metrology of Automated Tests Static and Dynamic Characteristics Viacheslav Karmalita, 2020 ISBN 978-3-11-066664-9, e-ISBN (PDF) 978-3-11-066667-0, e-ISBN (EPUB) 978-3-11-066669-4 Communication, Signal Processing & Information Technology Series: Advances in Systems, Signals and Devices, 12 Edited by Faouzi Derbel, Nabil Derbel, Olfa Kanoun, 2020 ISBN 978-3-11-059120-0, e-ISBN (PDF) 978-3-11-059400-3, e-ISBN (EPUB) 978-3-11-059206-1 Signal Processing and Data Analysis Tianshuang Qiu, Ying Guo, 2018 ISBN 978-3-11-046158-9, e-ISBN (PDF) 978-3-11-046508-2, e-ISBN (EPUB) 978-3-11-046513-6 Xian-Da Zhang Modern Signal Processing Author Prof. Xian-Da Zhang Tsinghua University Dept. of Automation Haidian District 1 Tsinghua Park 100084 Beijing People’s Republic of China Translation by Dong-Xia Chang Beijing Jiaotong University Ling Zhang Ocean University of China Dao-Ming Zhang LEIHUA Electronic Technology Institute ISBN 978-3-11-047555-5 e-ISBN (PDF) 978-3-11-047556-2 e-ISBN (EPUB) 978-3-11-047566-1 Library of Congress Control Number: 2022931618 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. © 2023 Tsinghua University Press Limited and Walter de Gruyter GmbH, Berlin/Boston Cover image: bestdesigns / iStock / Getty Images Plus Printing and binding: CPI books GmbH, Leck www.degruyter.com Acknowledgements WewouldliketothankMr.Yan-DaLi,AcademicianofChineseAcademyofSciences, IEEEFellow,andProfessorofDepartmentofAutomation,TsinghuaUniversity,forhis encouragementandstrongsupporttothetranslationofthisbook.Weareverygrateful tooureditorYi-LingWangforherpatience,understanding,andhelpinthecourseof ourtranslatingthisbook.WearegratefultoDr.Xi-YuanWangandDr.Fang-MingHan fortheirhelp.WewouldalsoliketothankJi-MinZheng,Ming-NuanQin,andHai-Zhou Wufortheirhelp. https://doi.org/10.1515/9783110475562-202 Contents 1 RandomSignals|1 1.1 SignalClassifications|1 1.2 CorrelationFunction,CovarianceFunction,andPowerSpectral Density|6 1.2.1 AutocorrelationFunction,AutocovarianceFunction,andPowerSpectral Density|6 1.2.2 CrossCorrelationFunction,CrossCovarianceFunction,andCrossPower SpectralDensity|10 1.3 ComparisonandDiscriminationbetweenTwoRandomSignals|13 1.3.1 Independence,Uncorrelatedness,andOrthogonality|14 1.3.2 Gram-SchmidtOrthogonalizationProcessofPolynomialSequence|18 1.4 LinearSystemwithRandomInput|19 1.4.1 ThePowerSpectralDensityofSystemOutput|19 1.4.2 NarrowBandBandpassFilter|22 Summary|25 Exercises|25 2 ParameterEstimationTheory|30 2.1 PerformanceofEstimators|30 2.1.1 UnbiasedandAsymptoticUnbiasedEstimation|31 2.1.2 EffectivenessofEstimators|33 2.2 FisherInformationandCramér-RaoInequality|35 2.2.1 FisherInformation|35 2.2.2 Cramér-RaoLowerBound|36 2.3 BayesEstimation|38 2.3.1 DefinitionofRiskFunction|39 2.3.2 BayesEstimation|40 2.4 MaximumLikelihoodEstimation|43 2.5 LinearMeanSquaresEstimation|47 2.6 LeastSquaresEstimation|49 2.6.1 LeastSquaresEstimationandItsPerformance|49 2.6.2 WeightedLeastSquaresEstimation|51 Summary|53 Exercises|53 3 SignalDetection|57 3.1 StatisticalHypothesisTesting|57 3.1.1 BasicConceptsofSignalDetection|57 3.1.2 SignalDetectionMeasures|61 VIII | Contents 3.1.3 DecisionSpace|65 3.2 ProbabilityDensityFunctionandErrorFunction|68 3.2.1 ProbabilityDensityFunction|69 3.2.2 ErrorFunctionandComplementaryErrorFunction|71 3.3 ProbabilitiesofDetectionandError|73 3.3.1 DefinitionsofDetectionandErrorProbabilities|74 3.3.2 PowerFunction|77 3.4 Neyman-PearsonCriterion|78 3.4.1 ProbabilitiesofFalseAlarmandMissalarminRadarSignal Detection|79 3.4.2 Neyman-PearsonLemmaandNeyman-PearsonCriterion|82 3.5 UniformlyMostPowerCriterion|86 3.5.1 CommunicationSignalDetectionProblem|86 3.5.2 UniformlyMostPowerTest|88 3.5.3 PhysicalMeaningofUMPCriterion|91 3.6 BayesCriterion|92 3.6.1 BayesDecisionCriterion|92 3.6.2 DetectionofBinarySignalWaveform|95 3.6.3 DetectionProbabilityAnalysis|98 3.7 BayesDerivedCriteria|100 3.7.1 MinimumErrorProbabilityCriterion|100 3.7.2 MaximumAPosterioriProbabilityCriterion|102 3.7.3 MinimaxCriterion|104 3.8 MultivariateHypothesesTesting|107 3.8.1 MultivariateHypothesesTestingProblem|108 3.8.2 BayesCriteriaforMultipleHypothesesTesting|109 3.9 MultipleHypothesisTesting|110 3.9.1 ErrorRateofMultipleHypothesisTesting|111 3.9.2 ErrorControlMethodofMultipleHypothesisTesting |114 3.9.3 MultipleLinearRegression|116 3.9.4 MultivariateStatisticalAnalysis|120 Summary|125 Exercises|125 4 ModernSpectralEstimation|132 4.1 NonparametricSpectralEstimation|132 4.1.1 DiscreteStochasticProcess|133 4.1.2 Non-parametricPowerSpectrumEstimation|134 4.2 StationaryARMAProcess|135 4.3 PowerSpectralDensityofStationaryProcess|141 4.3.1 PowerSpectralDensityofARMAProcess|141 4.3.2 PowerSpectrumEquivalence|146 Contents | IX 4.4 ARMASpectrumEstimation|149 4.4.1 TwoLinearMethodsforARMAPowerSpectrumEstimation|150 4.4.2 ModifiedYule-WalkerEquation|151 4.4.3 SingularValueDecompositionMethodforAROrder Determination|154 4.4.4 TotalLeastSquaresMethodforARParameterEstimation|157 4.5 ARMAModelIdentification|160 4.5.1 MAOrderDetermination|160 4.5.2 MAParameterEstimation|163 4.6 MaximumEntropySpectrumEstimation|165 4.6.1 BurgMaximumEntropySpectrumEstimation|165 4.6.2 LevinsonRecursion|168 4.6.3 BurgAlgorithm|173 4.6.4 BurgMaximumEntropySpectrumAnalysisandARMASpectrum Estimation|174 4.7 PisarenkoHarmonicDecompositionMethod|177 4.7.1 PisarenkoHarmonicDecomposition|177 4.7.2 ARMAModelingMethodforHarmonicRecovery|180 4.8 ExtendedPronyMethod|182 Summary|188 Exercises|188 5 AdaptiveFilter|193 5.1 MatchedFilter|193 5.1.1 MatchedFilter|194 5.1.2 PropertiesofMatchedFilter|199 5.1.3 ImplementationofMatchedFilter|200 5.2 ContinuousTimeWienerFilter|201 5.3 OptimalFilteringTheoryandWienerFilter|203 5.3.1 LinearOptimalFilter|203 5.3.2 OrthogonalityPrinciple|205 5.3.3 WienerFilter|206 5.4 KalmanFilter|209 5.4.1 KalmanFilteringProblem|209 5.4.2 InnovationProcess|210 5.4.3 KalmanFilteringAlgorithm|212 5.5 LMSAdaptiveAlgorithms|214 5.5.1 DescentAlgorithm|214 5.5.2 LMSAlgorithmandItsBasicVariants|216 5.5.3 DecorrelationLMSAlgorithm|217 5.5.4 SelectionoftheLearningRateParameter|221 5.5.5 StatisticalPerformanceAnalysisofLMSAlgorithm|223 X | Contents 5.5.6 TrackingPerformanceofLMSAlgorithm|225 5.6 RLSAdaptiveAlgorithm|228 5.6.1 RLSAlgorithm|229 5.6.2 ComparisonbetweenRLSAlgorithmandKalmanFiltering Algorithm|232 5.6.3 StatisticalPerformanceAnalysisofRLSAlgorithm|234 5.6.4 FastRLSAlgorithm|235 5.7 AdaptiveLineEnhancerandNotchFilter|237 5.7.1 TransferFunctionsofLineEnhancerandNotchFilter|237 5.7.2 AdaptiveNotchFilterbasedonLatticeIIRFilter|239 5.8 GeneralizedSidelobeCanceller|242 5.9 BlindAdaptiveMultiuserDetection|244 5.9.1 CanonicalRepresentationofBlindMultiuserDetection|245 5.9.2 LMSandRLSAlgorithmsforBlindMultiuserDetection|246 5.9.3 KalmanAdaptiveAlgorithmforBlindMultiuserDetection|249 Summary|253 Exercises|253 6 Higher-OrderStatisticalAnalysis|259 6.1 MomentsandCumulants|259 6.1.1 DefinitionofHigher-orderMomentsandCumulants|259 6.1.2 Higher-orderMomentsandCumulantsofGaussianSignal|262 6.1.3 TransformationRelationshipsbetweenMomentsandCumulants|263 6.2 PropertiesofMomentsandCumulants|265 6.3 Higher-orderSpectra|270 6.3.1 Higher-orderMomentSpectraandHigher-orderCumulant Spectra|270 6.3.2 BispectrumEstimation|272 6.4 Non-GaussianSignalandLinearSystem|276 6.4.1 Sub-GaussianandSuper-GaussianSignal|276 6.4.2 Non-GaussianSignalPassingThroughLinearSystem|277 6.5 FIRSystemIdentification|280 6.5.1 RCAlgorithm|280 6.5.2 CumulantAlgorithm|284 6.5.3 MAOrderDetermination|288 6.6 IdentificationofCausalARMAModels|289 6.6.1 IdentificationofARParameters|290 6.6.2 MAorderDetermination|293 6.6.3 EstimationofMAParameters|296 6.7 HarmonicRetrievalinColoredNoise|299 6.7.1 CumulantDefinitionforComplexSignal|300 6.7.2 CumulantsofHarmonicProcess|302