數(shù)字信號(hào)處理_基于計(jì)算機(jī)的方法_第四版_sanjit-k.mitra_習(xí)題答案 第9章

1、Notfsale1SOLUTIONSMANUALtoaccompanyDigitalSignalProcessing:AComputerBasedApproachFourthEditionSanjitK.MitraPreparedbyChowdaryAdsumilliJohnBergerMarcoCarliHsinHanHoRajeevGhiMartinGaweckiChinKayeKohLucaLuccheseMyleneQueiro

2、zdeFariasTravisSmithCopyright?2011bySanjitK.Mitra.NopartofthispublicationmaybereproduceddistributedinanyfmbyanymeansstedinadatabaseretrievalsystemwithoutthepriwrittenconsentofSanjitK.Mitraincludingbutnotlimitedtoinanywko

3、therelectronicStagetransmissionbroadcastfdistancelearning.Notfsale3anotherpassbintherange€–π≤ω≤0.Howeverbecauseoftheoverlapofthetwospectraasimplefmulafthebedgescannotbederived.HLP(ejω)ωωpωsπ–ωp–ωs–πδs1δp1–δp0ωG(ejω)π–πδs

4、1δp1–δp0ωoωoωsωoωpωo?ωpωo?ωs9.6(a)€hp(t)=ha(t)?p(t)where€p(t)=δ(t?nT).n=?∞∞∑Thus€hp(t)=ha(nT)n=?∞∞∑δ(t?nT)..Wealsohave€g[n]=ha(nT).Now€Ha(s)=ha(t)e?st?∞∞∫dt€Hp(s)=hp(t)e?st?∞∞∫dt=ha(nT)δ(t?nT)e?st?∞∞∫dtn=?∞∞∑=ha(nT)e?snT

5、n=?∞∞∑.Comparingtheaboveexpressionwith€G(z)=g[n]z?nn=?∞∞∑=h(nT)z?nn=?∞∞∑weconcludethat€G(z)=Hp(s)s=1Tlnz.WecanalsoshowthataFourierseriesexpansionofp(t)isgivenby€p(t)=1Te?j(2πktT)k=?∞∞∑.Therefe€hp(t)=1Te?j(2πktT)k=?∞∞∑???

6、?????????????ha(t)=1Tha(t)e?j(2πktT)k=?∞∞∑.Hence€Hp(s)=1THasj2πktT????????????k=?∞∞∑.Asaresultwehave€G(z)=1THasj2πktT????????????k=?∞∞∑s=1Tlnz.(71)(b)Thetransfmationfromthe€splaneto€zplaneisgivenby€z=esT.Ifweexpress€s=σo