现代数字信号处理参考高深.pptx

现代数字信号处理

AdvancedDigitalSignalProcessing

10.4LEAST-MEAN-SQUAREADAPTIVEFILTERS高深201214362

10.4LEAST-MEAN-SQUARE-ADAPTIVE-FILTERS10.4.1DerivationInthissection,wederive,analyzetheperformance,andpresentsomepracticalapplicationsoftheleast-mean-square(LMS)adaptivealgorithm.OptimizationapproachTheestimatealsocanbeobtainedbystartingwiththeapproximationandtakingitsgradient.ThecoefficientadaptationalgorithmisThestep-sizeparameter2μisalsoknownastheadaptationgainGeometricapproachAttimenthefilterhasaccesstoinputvectorx(n),thedesiredresponsey(n),andthepreviousoroldcoefficientestimatec(n?1).Itsgoalistousethisinformationtodetermineanewestimatec(n)thatisclosertotheoptimumvectororequivalentlytochoosec(n)sothat

10.4LEAST-MEAN-SQUARE-ADAPTIVE-FILTERSwherewewanttoenegligibleasn→∞whichisknownasthenormalizedLMSalgorithm.Notethattheeffectivestepsizeistime-varying.TheLMSalgorithmfollowsifwesetandchooseLMSalgorithmTheLMSalgorithmcanbesummarizedaswhereμisadaptationstepsize

10.4LEAST-MEAN-SQUARE-ADAPTIVE-FILTERS10.4.2AdaptationinaStationarySOEthegoaloftheLMSadaptivefilteristoidentifytheoptimumfilterfromobservationsoftheinputx(n)andthedesiredresponseThetimeevolutionofthesequantitiesprovidessufficientinformationtoevaluatethestabilityandsteady-stateperformanceoftheLMSalgorithm.

10.4LEAST-MEAN-SQUARE-ADAPTIVE-FILTERSConvergenceofthemeancoefficientvectorbecauseowingtotheorthogonalityprinciple.Ifweassumethatx(n)andarestatisticallyindependent,simplifiestoEvolutionofthecoefficienterrorcorrelationmatrixTheMSDcanbeexpressedintermsofth