信号系统期末试卷(一)

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1、佗(/)=sin3兀t,也(》)=Supposetheinput兀(/)=1+2sin2/+cosl0z,deteiTninetheoutputy(z).mdtFigure1信号系统期末试卷（一）sinA7Ct7lt1.(12point)considerthesystemillustratedinFigure1,where说(/)=幺'"比(f)，包(『)Solution:M)=E)*九⑴*[包⑴-仏⑴]*九⑴=x(?)*[h,(z)-h.(f)]*//,(?)*h4(?)

2、z)-/^(z)]=cos(10/)M)=必(!)*也“)*%")]=cos(lOt)*[%("*%(/)胡严+丹）*［说（小认）］冷国（皿）"（沟）］

3、“严+*国脚）"0•呱“]2jco+l0je•严+丄jo)2>+10jgjio.•、・.((sin1/、•・・1.(10point)ConsiderthesystemillustratedinFigure2,supposeXytj=,Pv)債showninFigure3.I加丿(a)Determinethemaximumsamplinginterval

4、Tsuchthatx(()isrecoverablefromyp(/)(b)IfT=0.1second,sketchthespectrumofyp(Z)Figure2(c)IfT=0.1second,determineafilterH(jco)sothaty(/)=无⑴Figure3Solution:(a)儿⑴=E)P⑴㈠3(M)=(沟)*P(jco)"（阀=£2呗2禅/4）旳斗2护）&=一8k，出（阀詁£空讐尿—⑺兀k=YK/xsin加yin加—•1-/•So,itshallbesatisfiedwi

5、th2兀<2兀］T一2龙=>Tmax=0.5(b)IfT=0.1,then©二2龙/0.1二20龙(C)IfH(jco)=Ga(jo)),4^

6、ealandoddsignal.Thisimpliesthatjr(t+l)㈠X(jo))ejM=X(jco)<3x(」"))isanimageryandoddsignal.69+□X(—-,371"2,A1□(>)=y3兀—CO^OY£—3》oo⑹JX(jco)dco=2^x(0)=In―ooooXje)魯=fX(f)〃/=34.(6point)Determinethefunction,fortheLaplacetransformX(5)anditsassociatedregionsofconvergen

7、ce:pS+x(沪罟,e-eSolution:ROC:Re{$}>0X(s)=夕+厂,2厂二/小=l+l戶se—e1—eoox(f)=》(f)+2》(f-2-2/?)n=05.(12point)ConsideranLTIsystemwithinpulx[/i]=——2]andoutputy[n]=5[咒]+(1/2厂u[n-l](a)FindthesystemfunctionH(z)，indicatetheROCofH(z)(b)Determinetheunitimpulseresponseh[n],ist

8、hissystemstable?(c)Computetheoutputofthissystem,iftheinputsignalisx[n]=cos7inSolution:(a)x[同=5[加—(1/4)—2]㈠X(z)=l—右y[n]=^[n]+(l/2f"1u[h-1]oY(z)=1+z+1/2z-1/22

9、z

10、>-X⑵-(z-1/2)2'R°C：2(b)nu[n]㈠—z(z•召_d_dtz-12)f/•772匕-1/2)~9Z_㈠(z-1/2丁Stable!-1/21/2-zflY「7<->n

11、—况&(z-1/2)2(2丿L/]<2,(]、"u[n](/?+!)—w[n+l]•・•x[n]=cos(勿)=(一1)"(c)4Aj[n]=W(-l)(-ir=-(-ir6・(12point)Theinputx(f)andoutputy⑴ofastableLTIsystemarerelatedthroughtheblock-diagramrepresentationshowninFigure5.(a)Deter