自适应滤波器在噪声消除中的应用与研究

南昌航空大学硕士学位论文自适应滤波器在噪声消除中的应用与研究姓名：余荣贵申请学位级别：硕士专业：计算机应用技术指导教师：叶水生20080601I:LMSMATLABLMSLMSe,eLMSLMSIIABSTRACTAllsystemswillbeinfluencedbynoise.Howtoeffectivelyeliminatethenoiseisoneofhotsubjectsforyears.Noisesuppressionisclassifiedintotwoclasses:PassiveNoiseControlandActiveNoiseControl.Withthedevelopmentofcontrolsystemtheoryanddigitalsignalprocessing,ActiveNoiseControlputsconcentrationonadaptation.Theadaptivenoisecancelingsystemandtheadaptivelineenhancementsystemdevelopformtheadaptivefilteringsystem.Theycanimprovethequalityofsignalbypickingupanddetectingtheusefulsignalorcancelingnoiseintheenvironmentwhichwasinterferedbynoise.ThepaperstudiedtheActiveNoiseControlanditsapplicationmethodbasedonadaptivefilterapproach.Thepaperbeginswiththeprinciple,structureandapplicationofadaptivefilter.Basedontheprinciple,theLeastMeanSquare(LMS)isresearcheddeeply.Itisaimportantalgorithmofadaptivefilter.Theratiocinativeprocessandconvergenceperformanceofthealgorithmsisgiven.Parametereffectsonperformanceofthealgorithmarestudied.BasedontheMATLABplatformsimulationiscarriedoutfortheadaptivealgorithmsanalysisofconvergencerateandsteadystateerrorresultsaregivenundervariousconditions.Accordingly,meritsofthedifferentalgorithmsarediscussed.Duetothefactthattheconvergentspeedandsteady-stateerrorareaffectedbythefixedstep-sizeinclassicalLMSalgorithm,manynewalgorithmispresentedwithvariablestep-size.Someofthemestablishanon-linearfunctionalrelationshipbetweenstep-sizefactorµandthesystemoutputerrore.However,thesystemoutputerroreofeveryapplicationofadaptivefilteraredifferent,therefore,theirstep-sizefactorµaredifferent.Thedifferenceofstep-sizefactorµdecreasetheprocessingabilitytheLMSalgorithm.So,accordingtothecharacteristicoftheadaptivenoisecancelerandtheadaptivelineenhancement,twoimprovedalgorithmarepresentedwithvariablestep-sizeLMSalgorithminthepaper,andthenanewimprovedalgorithmismadeupbythetwoimprovedalgorithm,Computersimulationverifiesthebetterperformanceofthenewimprovedalgorithm.Atthelast,thefilteroftheincorporationoftheadaptivenoisecancelerandtheadaptivelineenhancementisappliedtothesystemofelectricitymeasure.Emulationprovesthattheperformanceofdenoisingofthisfilerisexcellent.IIIKeyWords:self-adaptivefilter,TheLeastMeanSquarealgorithm,noisecanceling,lineenhancement1111.12060(FFT)2060([1])()[2][3-6]121.2[7]LMSWienerLMSLMSLMSLMS(LMSLeastMeanSquare)WidrowHoff1959LMSLMS[8-21]Harris1986LMS[8][10][11][12]ShariKaliathLMS[9]LMS(NormaliedLMS)LMSLMS(Nagumo&Noda1967;Douglas&Meng,1994)LMSLMS(fastblockLMSalgorithm:Clark1981,1983Ferrara1980)DCT-LMS[22](DiscreteCosnieTransformLMS)K-LLMS(GALGradientadaptivelattice)Griffits19771988LMS131.3MATLABLMS123LMSLMSLMS4LMSLMS5LMSLMS6LMS454572422019571960P.HowellsP.ApplebauB.WidrowM.HoffLMS1965[23],:():(MSE:MeanSquareError),:[24]()2.12.1.1Finite-durationImpulseResponse,FIR25Infinite-durationImpulseResponse,IIRFIRIIRFIRFIRIIR:(1)FIR;IIR(2)FIR;IIR(3)FIR:IIRFIRFIR2-12-1xL-1kLTx(k)[x(k),x(k-1),,x(k-L+1)]@L(2-1)TL26T12L-1w(k)[W(k),W(k),,W(k)]@L2-2kL-1Tii=0y(k)w(k)x(k-i)=w(k)x(k)∑@(2-3)2.1.22.1.1e(k)x(k),y(k)d(k)F=F[e(k)]=F[e(x(k),y(k),d(k))](2-4)2-5w(k+1)=w(k)+G[F(e(k))](2-5)G[F(e(k))]F(e(k))e(k)F(e(k))WienerKalmanSquare,LSLMS2.1.327()2-22-22-2x(n)y(n)d(n)e(n)y(n)d(n)e(n)2.1.4(1)kw(k)w0w(k)w0(2)w(k)w0(3)w(k)w0(4)28w(k)2.22.2.1(LMS)1()MSE22TTJ(n)=E[e(n)]d(n)-2wP+wRw=(2-6)TR=E[x(n)x(n)];P=E[d(n)x(n)]J(n)RPww0Rw0:-10w=RP(2-7)J(n)2.3292-32i{w(n)},i=0,1,,M-1L[25]:J(n)J(n)=-2P+2Rw(n)w(n+1)∂∇=∂(2-8)1w(n+1)=w(n)+[-J(n)]=w(n)+[P-Rw(n)]2(2-9)(2-9)µ210RP2LMSLMS[26]2J(n)=e(n))(2-10)Te(n)=d(n)-x(n)w(n)(2-11):2[e(n)]J(n)=2(n)e(n)w(n)x∂∇=−∂))(2-12)1w(n+1)=w(n)+[-J(n)]=w(n)+x(n)e(n)2(2-13)(2-11)(2-13)LMSWidrowHoff1959LMSLMSLMSµM-1ii=0220=tr[R]∑(2-14)(2-14)i{w(n)},i=0,1,,M-1LRnWO(Misadjustment)ξJex()JminexminE[J()]=J(2-15)(τmse)av2µλav,211M-1kk=01M∑,:avmseavM1==M4()2(2-16)(2-16)ξµmseavav1()=2µ;µµLMSλmax/λminLMSLMSLMS2.2.2LMSLMSLMSDentino1979[27]Narayan[28]1)2)3)TNnxnxnxnX)]1(,),1(),([)(+−−=ΛT)]([)(nxTnX⋅=TN*NHartlyWslsh-Hadamard)()(nwTnW⋅=)()()(nXnWnyT⋅=)()()(nyndne−=212)()()(2)()1(1nXnpnuenWnW−+=+(2-17))]1,()1,()0,([)(−=NnPnPnPdiagnPΛ(2-18)),(),()1(),1(),(lnXlnXlnPlnPT⋅−+−=ββl=0,1,N-1)(2nP=Λ,:)()(2)()1(2nXnuenWnW−Λ+=+(2-19)2.2.3(RLS)LMSRLSW(n)21|)(|)(ienJniin∗=∑=−λRLSRxx(n)RLSRxx(n)RLSRLSRLSRLS(Fast-RLS)[30][31](FastRecursiveleastSquaresLattice)[29]RLSRLsRLSRLSRLSFIRFIR213RLSRLSRLSRLSRLSRLSRLSLMS2.2.4RLSRLSRLSRLSRLSRLSAlan[32]2.2.5K.OzekiT.Umeda[33](NLMS)LMSRLSRLS(NLMS)LMSNLMSLMSNLMSP:)]1()1()[()(−∆+−=kWkWkXkYT(2-20))]1(,),1(),([)(+−−=PkykykykYΛ)]1(,),1(),([)(+−−=PkxkxkxkXΛW(k-1),214)1()()()(−−=kWkXkYkeT(2-21))(])()([)(1keIkXkXkgT−+=δ(2-22))()()1()1()1()(kgkuXkWkWukWkW+−=−∆+−=(2-23)(P+1)N+O(p3)RLSNLMSGay[34,35]Douglas[36]2.2.6[37]LMFRLF[38]Leaky-LMS[39]LMS(NLMS)2.3,2.3.12152fc02fc0FIR2-42-4x(n)d(n)W(n)2.3.22-52-5216(2-5)(LMS)2-62.4LMS2fc0+3LMS173LMS3.13.1.1MATLABMATLAB[40][41]MathWorksMATLABMATrixLABoratory()MATLABMATLAB:1MATLAB/2MATLABMATLAB.m3MATLAB2D3DMATLABMATLAB(GUI)4MATLABMATLAB5MATLABMATLABMATLABCFORTRANMATLAB()MATMATLABMATLAB3LMS183.1