1、北 京 交 通 大 学 考 试 试 题课程名称：信号与系统 姓名： 学号： 班级： 成绩： 题 号 一 二 三 四 五 六 七 八 九 十 总分得 分阅卷人一、填空题（每题 3 分，共 30 分）1 dtute)1(42.2 x1(n)=1,3,3；n= 1,0,1, x2(n)=1,4；n= 1,0，determine x 1(n)*x2(n) = .3Consider sampling )0Satt，determine the maximum of sampling interval T so that there will be no aliasing mxT (s).4A LTI sy
2、stem has input (si(tut and output )incos()tetyt，determine the impulse response of this system )(th .5A system has input 1and output )1ty. If the system has properties, then the input and output pairs has the relationship: input is 3)2()112txtx, so output is 3()2()112ttyt 。6The transfer function of a
3、 LTI system is)(sH, the system belongs to type . （high-pass, low-pass, band-pass or band-stop ?）7the FS of )(txis )jX, the FS of is jeX)2。8. the impulse response of integrator is ，the impulse response of differentiator is , the impulse response of discrete-time time-shift operator is 。9. )2(8.0)(nu，
4、determine )(je= 。 10 73sico1nx，Sketch the magnitude spectra )(kX, where )(kXis DTFS coefficients of x(n).二、简单计算题（每题 6 分，共 30 分）1x ( t ) is shown in following figure. Sketch x (2 2t )u (-t) and write out the brief steps.)(tx t1120t)()2( tutx02 )(txand th are shown in following figure. Suppose )(*)(ht
5、xy. Sketch )(ty。-101 t1x(t) )(tht212203 )(2)( ,()(1 nuhnuh. Determine )(nh, the impulse response of this system。 1(n)h 2hx y(n) (n)(n) +5 )(jH, frequency response of a LTI system, is shown in following figure. Input is )(),3cos5)2s(4)co(32 tttttx. Determine the output y(t)。)(jH840-4 三、计算题（40 分）1 （12
6、 分）A LTI system is described by following difference equation: )(2(61)(5) nxynyinput is ()nux，initial conditions are 0, compute in Z-domain:(1) Transfer function zH, impulse response )h;(2) (yzi, zs and )y.2 （14 分）A LTI system is described by following differential equation:)(2)(45(“ txtytt ，input i
7、s )(tux，initial conditions are 40,0 , compute in S-domain：(1) Transfer function )s. Is the system stable?(2) tyzi, tzs and (ty;(3) Draw direct form implementation for the system.3 （14 分）Consider amplitude modulation. A modulated signal is ttxgcos)(. In this equation )(1)(tmAtxcwhere 1c and the modulating signal m05srad/020 and srad/023.(1) Sketch tg;(2) Sketch )(jG, the FS of )(tg;（3）A LTI system has frequency response )190()19()uujH. If (tg is the input, determine the output ty.
