大二 數(shù)字信號(hào)處理Chapter 7 LTI DiscreteTime Systems in 專業(yè)知識(shí)講座

Chapter7LTIDiscrete-TimeSystemsintheTransformDomain第1頁(yè)FIRfilterIIRfilterClassificationbasedonthelengthoftheimpulseresponseh(n)inthetimedomainThereareseveralothertypesofclassificationsoftransferfunctionsbasedontheirmagnitudecharacteristics.Likewise,thereareseveralothertypesofclassificationsoftransferfunctionsbasedontheirphasecharacteristics.第2頁(yè)7.1TransferFunctionClassificationBasedonMagnitudeCharacteristics第3頁(yè)7.1.1DigitalFilterswithidealMagnitudeResponse第4頁(yè)第5頁(yè)第6頁(yè)Exercise:IfH(z)isalowpassfilterwithpassbandedgefrequencywc,determinethetypeoffilterH(-z)anditsbandedgeofH(-z)intermsofthebnadedgeofH(z)第7頁(yè)P(yáng)assbandStopbandCutofffrequencyTransitionbandThespecificationsinthetransformdomainiscorrespondingto第8頁(yè)7.1.2BoundedRealTransferFunctionspassivestructure第9頁(yè)7.1.3AllpassTransferFunctionTransferfunction?第10頁(yè)Supposeithasapoleattheremustbeazeroatmirror-imagesymmetrymirror-imagepolynomial第11頁(yè)Considera3-orderallpassfilter,andsupposeweknowittwopoles,complementtheremainingpolesandzerosofthesystem.

第12頁(yè)第13頁(yè)ShowthatisaAllpasssystemproof:第14頁(yè)Example:A3-orderAllpasssystem第15頁(yè)Exercise:ConsiderN(z)isthenumeratorfunctionofa3-ordercausalreal-coefficientallpasstransferfunction,andN(z)=0.32+0.075z-1+0.63z-2+z-3,determinethedenominatorfunctionofthisallpassfunction.1+0.63z-1+0.075z-2+0.32z-3D(z)=第16頁(yè)第17頁(yè)第18頁(yè)Asimpleapplication:delayequalizer第19頁(yè)7.2TransferFunctionClassificationBasedonPhaseCharacteristics第20頁(yè)7.2.1Zero-PhaseTransferFunctionnoncausalsystem第21頁(yè)第22頁(yè)7.2.2Linear-PhaseTransferFunctiony[n]=x[n-D]第23頁(yè)第24頁(yè)7.2.3Minimum-PhaseandMaximum-PhaseTransferFunctionAnotherusefulclassificationofatransferfunctionisbasedonthelocationofitszeros,which,inturn,influencesitsphaseresponse.第25頁(yè)第26頁(yè)第27頁(yè)第28頁(yè)7.3TypesofLinear-PhaseFIRTransferFunction第29頁(yè)Q1:ToinsureaFIRfilterhaslinear-phase,therestrictionofh[n]?Q2:TheformoffrequencyresponseofLinear-Phasefilter?第30頁(yè)7.3.1FrequencyResponseforaFIRFilterwithaLinear-PhaseWhere=±第31頁(yè)h[n]=±h[N-n],0≤n≤Nc=-N/2=±第32頁(yè)第33頁(yè)Examples:H1(z)=-0.0637-0.0691z-1+0.101z-2+0.2857z-3+0.4107z-4+0.2857z-5+0.101z-6-0.0691z-7-0.0637z-8H2(z)=-1+2z-1-3z-2+6z-3-3z-4+2z-5-z-6H3(z)=1-2z-1+3z-2-3z-4+2z-5-z-6第34頁(yè)7.3.2ZeroLocationsofLinear-PhaseFIRTransferFunctionMirror-ImageandAntimirror-ImagePolynomials第35頁(yè)Forsymmetrysequenceh[n]=h[N-n]WhichtypesofFIRFilterhaveMIPproperty?第36頁(yè)Forantisymmetrysequenceh[n]=-h[N-n]WhichtypesofFIRFilterhaveAIPproperty?第37頁(yè)Moreover,foraFIRfilterwithrealimpulseresponseh[n],itszerosoccurincomplexconjugatepairs第38頁(yè)·forcomplexzerothatisnotontheunitcircle,itsassociatedwithasetof4zerosForrealzero,it’sapairwithreciprocalz=ξ,z=1/ξ第39頁(yè)FortypeIfilter,itsMIPisevendegree,henceithasfactorsoftheform(1+az-1+bz-2+az-3+z-4)and(1+cz-1+z-2),soitcanhaveanevennumberofzerosornozerosatz=z-1oratz=-z-1,orbothlocations.第40頁(yè)H(z)musthaveazeroatz=-1第41頁(yè)Fortype3FIRfilter,NisevenH(z)musthaveazeroatz=-1andz=1第42頁(yè)Fortype4FIRfilter,NisoddH(z)musthaveazeroatz=1第43頁(yè)第44頁(yè)第45頁(yè)第46頁(yè)第47