数字信号处理(英文版)教学课件8-Infinite-Impulse-Response-Filters

UnderstandingDSP,SecondEditionChapter8InfiniteImpulseResponseFiltersUnderstandingDSP,SecondEditionOutline28.1AnIntroductiontoInfiniteImpulseResponseFilters8.2TheLaplaceTransform8.3AnalogLow-PassFilters8.4ImpulseInvarianceIIRFilterDesignMethod8.5BilinearTransformIIRFilterDesignMethod8.6Low-PassIIRFilterDesign8.7OtherTypesIIRFilterDesignUnderstandingDSP,SecondEdition8.1AnIntroductiontoInfiniteImpulseResponseFiltersInfiniteimpulseresponse(IIR)digitalfiltersarefeedbacksystem.IIRfilteroutputsampledependsonpreviousinputsamplesandpreviousfilteroutputsamples.ThecharacteristicofIIRfilters:1)Morecomplicatedstructures2)Hardertodesignandanalyze3)Donothavelinearphaseresponses3UnderstandingDSP,SecondEditionIIRfiltersareveryefficient4UnderstandingDSP,SecondEditionFIRdigitalfilterstructures(a)TraditionalFIRfilterstructure;(b)Rearranged,butequivalent,FIRfilterstructure.5UnderstandingDSP,SecondEditionIIRdigitalfilterstructuresIIRfiltersspreviousoutputsamplesareusedtocalculatethecurrentoutputsample.StandardIIRfilterdesigntechniquesfallintothreebasicclasses:1)theimpulseinvariance2)bilineartransform3)optimizationmethods6UnderstandingDSP,SecondEditionIIRdigitalfilterstructures7UnderstandingDSP,SecondEditionThese design methods use a discretesequence,mathematicaltransformationprocess known as the z-transform whoseoriginistheLaplacetransformtraditionallyusedintheanalyzingofcontinuoussystems.8UnderstandingDSP,SecondEdition8.2TheLaplaceTransformTheLaplacetransformisamathematicalmethodofsolvinglineardifferentialequationsthathasprovedveryusefulinthefieldsofengineeringandphysics.ThefundamentalprocessStep1.Atime-domaindifferentialequationiswrittenthatdescribestheinput/outputrelationshipofaphysicalsystemStep2.ThedifferentialequationisLaplacetransformed,convertingittoanalgebraicequation9UnderstandingDSP,SecondEdition10Step3.StandardalgebraictechniquesareusedtodeterminethedesiredoutputfunctionsequationintheLaplacedomainStep4.ThedesiredLaplaceoutputequationistheinverseLaplacetransformedtoyieldthedesiredtime-domainoutputfunctionsequationUnderstandingDSP,SecondEditionTheLaplacetransformofacontinuoustime-domainfunctionf(t),wheref(t)isdefinedonlyforpositivetime(t0),isexpressedmathematicallyas11SisthecomplexnumberUnderstandingDSP,SecondEdition12UnderstandingDSP,SecondEditionLinearsystemThebeautifulpropertyofLaplacetransform13UnderstandingDSP,SecondEditionIfweletx(t)andy(t)befunctionsofestPolynomialsthetransferfunction14UnderstandingDSP,SecondEditionAllinputfunctionscanberepresentedwithcomplexexponentialsAconstant,Amonotonicexponential,Anexponentiallyvaryingsinusoid,15UnderstandingDSP,SecondEditionAssumethecoefficientsareallreal,andb1anda2areequaltozero.Thiss=-a0/a1pointonthes-planeiscalledapolePolelocatedats=s+jw=-a0/a1+j0onthes-planeTime-domainy(t)impulseresponseofthesystem.16UnderstandingDSP,SecondEdition17UnderstandingDSP,SecondEditionTheLaplacetransformisamoregeneralcaseoftheFouriertransformThe|H1(s)|curvefors=0abovethes-planebecomesthe|H1(w)|curveabovethejwaxis18UnderstandingDSP,SecondEditionFurtherdepictionsofH1(s)(a)Polelocatedats=-a0/a1onthes-plane;(b)|H1(s)|surface;(c)Curveshowingtheintersectionofthe|H1(s)|surfaceandtheverticals=0plane.Thisistheconventionaldepictionofthe|H1(w)|frequencymagnituderesponse.19UnderstandingDSP,SecondEditionDescriptionsofH2(s)(a)Poleslocatedats=prealjpimagonthes-plane(b)Timedomainy(t)impulseresponseofthesystem20UnderstandingDSP,SecondEdition21UnderstandingDSP,SecondEditionFurtherdepictionsofH2(s)(a)Polesandzerolocationsonthes-plane(b)|H2(s)|surface(c)|H2(s)|Frequencymagnituderesponsecurve22UnderstandingDSP,SecondEditionVariousH(s)polelocationsandtheirtime-domainimpulseresponses23UnderstandingDSP,SecondEdition248.3AnalogLow-PassFiltersWhatwewillstudy:8.3.1Introduction8.3.2Approximationofanalogfiltercharacteristics8.3.3ButterworthApproximation8.3.4ChebyshevApproximationUnderstandingDSP,SecondEdition25WhywestudyAFfirstly?DFistheimportantapplicationinDSP，butdevelopedinrecent20-30years;Usingknowledgeaboutanalogyfilter，whichhasbeendevelopedalongtimeagoandmaturenow;Sofirstly，wediscusstheapproximationofanalogyfiltercharacterbeforestudyDF.8.3.1IntroductionUnderstandingDSP,SecondEdition26DesigningprincipleforIIRDFTwodesigningmethodsforIIRfilterMethod1：AnalogybandtransitionA/DtransitionAnalogyLPdesignIIRfilteringMethod2：AnalogyLPdesign(s)A/DTransition(sz)DigitalbandTransition(zz)IIRfiltering UnderstandingDSP,SecondEdition27Filters:classificationFilter：allowthewantedsignalinoneormorefrequency bands to pass while suppress theunwantedsignalinotherbandspassstoptransitionPassband：frequencybandsthesignalcanbepassed.“cut-offfrequency”isattheedgeofpassbandStopband：frequencybandsblockthesignalTransitionband：frequencybandrangefrompassbandtostopbandUnderstandingDSP,SecondEdition28 Basedonthepassfrequencyband,thefiltercanbeclassifiedintofourtypes.a)Lowpassfilter：e.g.filteringoutbackgroundnoiseofthetaperecordb)High pass filter：e.g.filtering out the lowfrequencynoiseforsonarsystemc)Band-pass filter：e.g.Decoding of thedouble-tonemulti