2010年信号与系统a卷答案

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1、四川大学期末考试试题（闭卷）A卷答案（2009——2010学年第二学期）1TrueorFalseQuestion(10points)(1)x[n]=sin(3n/4)isaperiodic(非周期的)・(T)(2)TheFouriertransformofanaperiodicdiscrete-timesignalisperiodic(T)andcontinuous.(T)(3)AnLTIsystemwithfrequencyfunctionH(j6))=haslinearphase(线性相位).(T)(4)estistheeigenfuncti

2、on(特征函数)ofLTIsystems.(F)(5)Thecontinuous-timeFouriertransformofareal-evensignalisareal-evenfunction.(T)(6)Thediscrete-timeFouriertransformofareal-evensignalisanimaginary-oddfunction.(F)(7)IftheROC(收敛域)oftheLaplacetransformX(s)includestheunitcircleof「plane(s平面儿thenX(M)=X($)

3、“・

4、(F)(8)Ifx(t)isrealandifX(s)hasapole(极点)ats=SqthenX(s)alsohasapoleatthepointS=-5o.(F)(9)Adiscrete-timeLTIsystemisstableifandonlyiftheROCofitssystemfunctionH(z)includestheunitcircleofz-plane>(T)2BlankFilling(20points)(1)J(Z—1)*3(—t)=—.(2points)(2)If£["]={*2,3},x2[n]={l92,3,4}an

5、dy[n]=x}[n]*x2[n]thenthemaximumlengthofy[n]isQ•(2points)(3)Ifthespectrum-density(谱密度)functionofanaperiodiccontinues-timesignalx(t)isX(»=,thenthemagnitude(幅度)offrequencyresponseis29andthephase(相位)offrequencyresponseis一叽堆3(3points)(4)Expansioninthetimedomaincorrespondingtocompr

6、essing(Compressing,Expansion)inthefrequencydomain.(2points)Ifx(t)―>X,thenx(t)cos<》邑妙迥譽也如1.（2points）(6)Ifx(t)<_-~~>X(jd))^thentheinverseFurioustransform(傅里叶反变换)ofX[j(d)—©)]isx(t)ejMot•(2points)(7)ConsideranLTIsystemwithunitimpulseresponseh[n]=allu[n]9

7、a

8、<1•Thefrequencyresponse

9、ofthesystemis•Thesystemisalowpass(highpass.lowpassorbandpass)1-a严filter.(4points)(8)Suppose工J/)andx2(t)arebandlimitedtoG)2respectively^thatisX[(J6W)=0,

10、Q2禺，X2(jd?)=0,

11、

12、>.Underthesamplingtheorem,theminimumsamplingfrequency(最小采样频率)is="①十or©=2(©+购)・Gpoints)2龙3.Calculation(70poin

13、ts)3.1(15points)Letx(t)betheinputtoanLTIsystemwithunitimpulseresponseh(t)ywherex(Z)=e~2tu{t)and〃(『)=“(/)・Calculatingtheoutputofthesystemy(t)byuseofconvolutionintegralequation(卷积公式)，butnotFourierTransformorLaplaceTransform.解:y(t)=x(r)h(t-T)dT=rJ—8J—8e^2Tu(r)u(t-t)dt当/>0时y(t)=£

14、e~2Tdt=-(l-产)o23.2(15points)Supposewearegiventhefollowinginformation