数字信号处理a(双语)chapter6-ztransformb.ppt

6.7.3FrequencyResponsefromTransferFunctionItisconvenienttovisualizethecontributionsofthezerofactor(z-?k)andthepolefactor(z-?k)fromthefactoredformofthefrequencyresponseThemagnitudefunctionisgivenbyFrequencyResponsefromTransferFunctionThephaseresponseforarationaltransferfunctionisoftheformThemagnitude-squaredfunctionofareal-coefficienttransferfunctioncanbecomputedusingGeometricInterpretationofFrequencyResponseComputationThefactoredformofthefrequencyresponseisconvenienttodevelopageometricinterpretationofthefrequencyresponsecomputationfromthepole-zeroplotasωvariesfrom0to2πontheunitcircleGeometricInterpretationofFrequencyResponseComputationThegeometricinterpretationcanbeusedtoobtainasketchoftheresponseasafunctionofthefrequencyAtypicalfactorinthefactoredformofthefrequencyresponseisgivenby(ejω-ρejΦ)whereρejΦisazeroifitiszerofactororisapoleifitisapolefactorAsshownbelowinthez-planethefactor(ejω-ρejΦ)representsavectorstartingatthepointz=ρejΦandendingontheunitcircleatz=ejωGeometricInterpretationofFrequencyResponseComputation6.4TheInversez-Transform6.5z-TransformTheoremsPartB:InverseZTandZTTheorems6.5z-TransformTheorems6.5z-TransformTheorems6.5z-TransformTheorems6.5z-TransformTheorems6.5z-TransformTheoremsPartC:ConvolutionComputationoftheConvolutionSumofFinite-LengthSequencesLinearConvolutionUsingPolynomialMultiplicationCircularConvolutionUsingPolynomialMultiplicationLinearConvolutionUsingz-TransformLetdenote{x[n]},0?n?L,afinite-lengthsequenceoflengthL+1Letdenote{h[n]}0?n?M,afinite-lengthsequenceoflengthM+1Weshallevaluatey[n]=x[n]*h[n]usingz-transformNote:{y[n]}isasequenceoflengthL+M+16.6.1LinearConvolutionUsingz-TransformLe