FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧

FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧2OutlineIntroductionIIRFilterDesignbyImpulseinvariancemethodIIRFilterDesignbyBilineartransformationmethodFIRFilterDesignbyWindowfunctiontechniqueFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧3OutlineFIRFilterDesignbyFrequencysamplingtechniqueFIRFilterDesignbyMSEConclusionsReferencesFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧4IntroductionBasicfilterclassificationWeputemphasisonthedigitalfilternow,andwillintroducetothedesignmethodoftheFIRfilterandIIRfilterrespectively.FilterAnalogFilterDigitalFilterIIRFilterFIRFilterFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧5IntroductionIIRistheinfiniteimpulseresponseabbreviation.Digitalfiltersbytheaccumulator,themultiplier,anditconstitutesIIRfiltertheway,generallymaydivideintothreekinds,respectivelyisDirectform,Cascadeform,andParallelform.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧6IntroductionIIRfilterdesignmethodsincludetheimpulseinvariance,bilineartransformation,andstepinvariance.Wemustemphasizeatimpulseinvarianceandbilineartransformation.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧7IntroductionIIRfilterdesignmethodsContinuousfrequencybandtransformationImpulseInvariancemethodBilineartransformationmethodStepinvariancemethodIIRfilterNormalizedanaloglowpassfilterFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧8IntroductionThestructuresofIIRfilterDirectform1Directform2b0b1b2b2b1b0-a1-a2-a1-a2x(n)x(n)Y(n)Y(n)FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧9IntroductionThestructuresofIIRfilterCascadeformx(n)Y(n)b0b1b2-a1-a2-c1-c2d1d2ParallelformY(n)x(n)b1b0d1d0E-c1-c2-a1-a2FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧10IntroductionFIRisthefiniteimpulseresponseabbreviation,becauseitsdesignconstructionhasnotreturnedtothepartwhichgives.ItsconstructiongenerallyusesDirectformandCascadeform.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧11IntroductionFIRfilterdesignmethodsincludethewindowfunction,frequencysampling,minimizethemaximalerror,andMSE.Wemustemphasizeatwindowfunction,frequencysampling,andMSE.WindowfunctiontechniqueFrequencysamplingtechniqueMinimizethemaximalerrorFIRfilterMeansquareerrorFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧12IntroductionThestructuresofFIRfilterx(n)x(n)b1b2b3b4b0Y(n)Y(n)DirectformCascadeformb1b2d1d2b0FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧13IIRFilterDesignbyImpulseinvariancemethodThemoststraightforwardoftheseistheimpulseinvariancetransformationLetbetheimpulseresponsecorrespondingto,anddefinethecontinuoustodiscretetimetransformationbysettingWesamplethecontinuoustimeimpulseresponsetoproducethediscretetimefilterFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧14IIRFilterDesignbyImpulseinvariancemethodThefrequencyresponseistheFouriertransformofthecontinuoustimefunctionandhenceFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧15IIRFilterDesignbyImpulseinvariancemethodThesystemfunctionisItisthemany-to-onetransformationfromthesplanetothezplane.

FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧16IIRFilterDesignbyImpulseinvariancemethodTheimpulseinvariancetransformationdoesmapthe-axisandtheleft-halfsplaneintotheunitcircleanditsinterior,respectively

Re(Z)Im(Z)1SdomainZdomainFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧17IIRFilterDesignbyImpulseinvariancemethodisanaliasedversionofThestop-bandcharacteristicsaremaintainedadequatelyinthediscretetimefrequencyresponseonlyifthealiasedtailsofaresufficientlysmall.

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FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧18IIRFilterDesignbyImpulseinvariancemethodTheButterworthandChebyshev-IlowpassdesignsaremoreappropriateforimpulseinvarianttransformationthanaretheChebyshev-IIandellipticdesigns.Thistransformationcannotbeapplieddirectlytohighpassandbandstopdesigns.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧19IIRFilterDesignbyImpulseinvariancemethodisexpandedapartialfractionexpansiontoproduceWehaveassumedthattherearenomultiplepolesAndthusFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧20IIRFilterDesignbyImpulseinvariancemethodExample:Expandinginapartialfractionexpansion,itproduceTheimpulseinvarianttransformationyieldsadiscretetimedesignwiththesystemfunctionFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧21IIRFilterDesignbyBilineartransformationmethodThemostgenerallyusefulisthebilineartransformation.Toavoidaliasingofthefrequencyresponseasencounteredwiththeimpulseinvariancetransformation.Weneedaone-to-onemappingfromthesplanetothezplane.Theproblemwiththetransformationismany-to-one.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧22IIRFilterDesignbyBilineartransformationmethodWecouldfirstuseaone-to-onetransformationfromto,whichcompressestheentiresplaneintothestripThencouldbetransformedtozbywithnoeffectfromaliasing.sdomain

s’domainFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧23IIRFilterDesignbyBilineartransformationmethodThetransformationfromtoisgivenbyThecharacteristicofthistransformationisseenmostreadilyfromitseffectontheaxis.Substitutingand,weobtainFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧24IIRFilterDesignbyBilineartransformationmethodTheaxisiscompressedintotheintervalforinaone-to-onemethodTherelationshipbetweenandisnonlinear,butitisapproximatelylinearatsmall.-FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧25IIRFilterDesignbyBilineartransformationmethodThedesiredtransformationtoisnowobtainedbyinvertingtoproduceAndsetting,whichyieldsRe(Z)Im(Z)1SdomainZdomainFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧26IIRFilterDesignbyBilineartransformationmethodThediscrete-timefilterdesignisobtainedfromthecontinuous-timedesignbymeansofthebilineartransformationUnliketheimpulseinvarianttransformation,thebilineartransformationisone-to-one,andinvertible.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧27FIRFilterDesignbyWindowfunctiontechniqueSimplestFIRthefilterdesigniswindowfunctiontechniqueAsuppositionidealfrequencyresponsemayexpresswhereFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧28FIRFilterDesignbyWindowfunctiontechniqueTogetthiskindofsystematiccausal

FIRtobeapproximate,themostdirectmethodinterceptsitsidealimpulseresponse!FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧29FIRFilterDesignbyWindowfunctiontechniqueTruncationoftheFourierseriesproducesthefamiliarGibbsphenomenonItwillbemanifestedin,especiallyifisdiscontinuous.FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧30FIRFilterDesignbyWindowfunctiontechnique1.Rectangularwindow2.Triangularwindow(Bartettwindow)FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧31FIRFilterDesignbyWindowfunctiontechnique1.Rectangularwindow2.Triangularwindow(Bartettwindow)FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧32FIRFilterDesignbyWindowfunctiontechnique3.HANNwindow4.HammingwindowFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧33FIRFilterDesignbyWindowfunctiontechnique3.HANNwindow4.HammingwindowFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧34FIRFilterDesignbyWindowfunctiontechnique’swindow6.BlackmanwindowFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧35’swindow6.BlackmanwindowFIRFilterDesignbyWindowfunctiontechniqueFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧36FIRFilterDesignbyWindowfunctiontechniqueWindowPeaksidelobelevel(dB)TransitionbandwidthMax.stopbandripple(dB)Rectangular-130.9-21Hann-313.1-44Hamming-413.3-53Blackman-575.5-74FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧37FIRFilterDesignbyFrequencysamplingtechniqueForarbitrary,non-classicalspecificationsof,thecalculationof,n=0,1,…,M,viaanappropriateapproximationcanbeasubstantialcomputationtask.Itmaybepreferabletoemployadesigntechniquethatutilizesspecifiedvaluesofdirectly,withoutthenecessityofdeterminingFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧38FIRFilterDesignbyFrequencysamplingtechniqueWewishtoderivealinearphaseIIRfilterwithrealnonzero.TheimpulseresponsemustbesymmetricwherearerealanddenotestheintegerpartFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧39FIRFilterDesignbyFrequencysamplingtechniqueItcanberewrittenaswhereandTherefore,itmaywrite

whereFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧40FIRFilterDesignbyFrequencysamplingtechniquewithcorrespondingtransformwhereHencewhichhasalinearphaseFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧41FIRFilterDesignbyFrequencysamplingtechniqueThemagnituderesponsewhichhasamaximumvalueatwhere

FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧42FIRFilterDesignbyFrequencysamplingtechniqueTheonlynonzerocontributiontoatisfrom,andhencethatTherefore,byspecifyingtheDFTsamplesofthedesiredmagnituderesponseatthefrequencies,andsettingFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧43FIRFilterDesignbyFrequencysamplingtechniqueWeproduceafilterdesignfromequation(5.1)forwhichThedesiredandactualmagnituderesponsesareequalattheNfrequenciesFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧44FIRFilterDesignbyFrequencysamplingtechniqueInbetweenthesefrequencies,isinterpolatedasthesumoftheresponses,anditsmagnitudedoesnot,equalthatofFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧45FIRFilterDesignbyFrequencysamplingtechniqueExample:Foranideallowpassfilterfrom,wewouldchooseThefrequencysamplesareindeedequaltothedesiredFIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧46FIRFilterDesignbyFrequencysamplingtechniqueTheresponseisverysimilartotheresultformusingtherectangularwindow,andthestopbandissimilarlydisappointing.Wecantrytosearchfortheoptimumvalueofthetransitionsamplewouldquicklyleadustoavalueofapproximately,FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧47FIRFilterDesignbyMSE:Thespectrumofthefilterweobtain:ThespectrumofthedesiredfilterMSE=FIRandIIRFilterDesignTechniquesFIR和IIR滤波器相关设计技巧48FIRFilterDesignbyMSE