大二 數(shù)字信號處理課件chapter 6 zTransform

chapter6z-Transform第1頁6.1DefinitionandProerties第2頁第3頁第4頁Example6.3Determinethez-Transformofafinite-lengthSolution:ROC:theentirez-planeexceptpossiblyz=0andz=∞第5頁第6頁6.2Rationalz-Transforms

第7頁transformfunctionmodelzero-polemodel第8頁theconceptofzeroandpolethecomplexzerosandpolesofrationalZTwithrealcoefficientsoccurascomplexconjugatepairs,andsimplepolesandzerosarereal.第9頁6.3ROCofaRationalz-TransformwithouttheconceptofROC,thereisnouniquerelationshipbetweenx(n)andX(Z);iftheROCofX(Z)isincludeunitcircle,ZTDTFT;theROCofarationalZTisboundedbythelocationofitspoles第10頁TheROCoftheZTofafinite-lengthsequencedefineforM≤n≤Nistheentirez-planeexceptpossiblez=0and/orz=∞.TheROCoftheZTofaright-sidedsequencedefinedforM≤n<∞isexteriortoacircleinthez-planepassingthroughthepolefurthestfromtheoriginez=0TheROCoftheZTofaleft-sidedsequencedefinedfor∞<n≤Nisinteriortoacircleinthez-planepassingthroughthepolenearesttotheoriginez=0TheROCoftheZTofatwo-sidedsequenceofinfinitelengthisringboundedbytwocirclesinthez-planepassingthroughtwopolesinsidethering第11頁Question:DeterminethefollowingthreeROCscorrespondingtowhichkindofsequencesrespectively.第12頁Exercise:P2956.24第13頁MATLABM-file:zplane(zeros,poles);zplane(num,den);[num,den]=zp2tf(z,p,k)MATLABprogramProgram_6.1,Program_6.2第14頁6.4TheInversez-Transform第15頁6.4.1GeneralExpression第16頁6.4.2Inversez-TransformbyTableLook-upMethod第17頁6.4.3Inversez-TransformbyPartial-FractionExpansionIfthedegreeMofthenumeratorpolynomialP(z)isgreaterthanorequaltothedegreeNofthedenominatorpolynomialD(z),therationalfunctionP(z)/D(z)iscalledanimproperfraction.第18頁properfraction第19頁Example6.13Determine

theProperFractionofaRationalz-Transform第20頁◎simplepoles第21頁Example6.14Inversez-TransformComputationviaPartial-FractionExpansion.第22頁◎MultiplePoles第23頁6.4.4Partial-FractionExpansionUsingMATLAB第24頁MATLABexampleprogram_6.3,program_6.4第25頁6.4.5Inversez-TransformviaLongDivision第26頁6.4.6Inversez-TransformUsingMATLAB第27頁6.5z-TransformProperties第28頁第29頁第30頁Example6.23Determinethez-Transformofasumoftwocausalexponentialsequences第31頁Determineitsz-TransformandROC第32頁Example6.25Determinethez-TransformV(z)ofthesequencev(n)givenbythefollowingequation第33頁第34頁Example6.27Determinetheinversez-transformofarationaltransformwithMultiplePoles第35頁Example6.28EnlargementofROCcausedbyPole-ZeroCancellation.ROC:|z|>0.2第36頁6.6ComputationoftheconvolutionsumofFinite-lengthSequences第37頁Example6.30第38頁6.7TheTransferFuncionFrequencyresponseTransferfunction第39頁6.7.1DefinitionLTIδ(n)h(n)x(n)y(n)describeasystemintimedomainZT第40頁第41頁6.7.2TransferFunctionExpressionFIRDigitalFilterh[n]isdefinedforN1toN2Question:TheROCofaFIRfiltertransferfunction?第42頁ROC?第43頁6.7.2TransferFunctionExpressionFinite-DimensionalLTIDiscrete-TimeSystme第44頁第45頁第46頁6.7.3FrequencyResponsefromTransferFunction第47頁第48頁第49頁6.7.4GeometricInterpretationofFrequencyResponseComputation第50頁第51頁Exercise:Plotthemagnituderesponseofasystemwiththezerosandpolesshownbelow.Zplane第52頁6.7.5StabilityConditioninTermsofPoleLoationForcausalsystem,AllpolesofH(z)isinsidetheunitcircleForanticausalsystem,AllpolesofH(z)isoutsidetheunitcircle第53頁Exercise:Consideralength-3sequenc