數(shù)字信號(hào)處理-基于計(jì)算機(jī)的方法(第四版)答案 8-11章

1、1SOLUTIONSMANUALtoaccompanyDigitalSignalProcessing:AComputerBasedApproachFourthEditionSanjitK.MitraPreparedbyChowdaryAdsumilliJohnBergerMarcoCarliHsinHanHoRajeevGhiMartinGaweckiChinKayeKohLucaLuccheseMyleneQueirozdeFaria

2、sTravisSmithCopyright?2011bySanjitK.Mitra.NopartofthispublicationmaybereproduceddistributedinanyfmbyanymeansstedinadatabaseretrievalsystemwithoutthepriwrittenconsentofSanjitK.Mitraincludingbutnotlimitedtoinanywkotherelec

3、tronicStagetransmissionbroadcastfdistancelearning.3(a)Sincethetransferfunctionissecondderthestructureisnoncanonic.(b)€H(ej0)=K(?d2d11)1d1?d2=K.Hencethestructurehasaunitygainatω=0ifK=1.(c)€H(ejπ)=K(?d2?d11)1?d1?d2=K.Hence

4、thestructurehasaunitygainatω=πifK=1.(d)Ifwelet€D(z)=1d1z?1?d2z?2then€H(z)=Kz?2D(z?1)D(z).Now€H(z)H(z?1)=Kz?2D(z?1)D(z)?Kz2D(z)D(z?1)=K2.Thisimplies€H(ejω)2=H(z)H(z?1)z=ejω=K2inotherwdsthetransferfunctionhasaconstantmagni

5、tudefallvaluesofω.8.5Thestructurewithinternalvariablesisshownbelow.Analysisofthisstructureyields€V(z)=γ2X(z)U(z)€U(z)=k1Y(z)γ1X(z)€Y(z)=z?1V(z)k2z?1U(z).Eliminatingtheinternalvariableswearriveat€H(z)=Y(z)X(z)=[(1k2)γ1γ2]

6、z?11k1(1k2)z?1.Fstabilitywerequire€k1(1k2)1.8.6AnequivalentrepresentationofthestructureofFigureP8.4withinternalvariablesisshownbelow.Analysisofthisstructureyields€U(z)=X(z)α0(z?1?1)W(z)€W(z)=α1(z?1?1)U(z)?Y(z)€Y(z)=U(z)?