山大 信号与系统 2008 试卷

Signal and system test paper B (08-09)一、PART 1 CHOOSING THE BEST ANSWER (25 points)1.The following signals are shown below, the ______is periodic signal.A.x(t)=costu(t)B.x[n]=cos(1/4)nC.X(Ω)=The Fourier transform of x[n]2.The Fourier transform of periodic signal x T(t) is_______ .A. discrete values c kB. impulse train（冲激序列）C. continuous function3.The frequency transfer function of the ideal filter is given by│H(ω)│=0 for -B≤│ω│≤B,│H(ω)│=1 for │ω│≥Bthe ideal filter is_________.A. a high-pass filterB. a band-stop filterC. a low-pass filter4.The input/output relationship of the discrete-time system in time domain is______.A. The Fourier transform representation and the convolution model.B. The input/output differential equation and the convolution model.C. The input/output difference equation and the convolution model.5.The rectangular pulse train is periodic signal with fundamental period T. Theamplitude spectrum is |Ck|. When T becomes large, Then________A. |Ck| becomes larger and the line spectrum interval (谱线间隔) becomeslargerB. |Ck| becomes smaller and the line spectrum interval becomes largerC. |Ck| becomes smaller and the line spectrum interval becomes smaller6.Suppose that x(t) is given by x(t)={x1(t) t1≤t﹤t2 and x2(t) t≥t2}.The signal x(t) can be expressed _______.A. x(t)=x1(t)[u(t-t1)- u(t-t2)]+ x2(t)[u(t-t1)- u(t-t2)]B. x(t)=x1(t)[u(t-t1)- u(t-t2)]+ x2(t)u(t-t2)C.x(t)=[x1(t) + x2(t)][u(t-t1)- u(t-t2)]7.The discrete-time system hes the relationship with the input and theoutput .y[n]= nx[n].To determined the system are _______.A. linear,causal,time varying , memorylessB. nonlinear,causal,time varying, memoryC. linear,causal, time invariant, memoryless8. The magnitude function of the ideal lowpass filter is 1 for|ω|<B, the time delay is t d for all frequency. The input signal tothe ideal lowpass filter is δ(t), the Fourier transform Y(ω) of theresponse y(t) is ______.A. 1, for allω.B. d-j ωt e ,for |ω|<BC. 1, for |ω|<B9. The relationship between the DTFT and DFT is _________.A. DTFT=DFTB.Ω=2π/N DFT=DTFT| C. Ω=2πk/N DFT=DTFT|, k=0,1…N -1 10. For a stable linear time-invariant system, the steady state response must inthe______.A. zero input responseB. zero state responseC. zero input and zero state response二 、ANSWER THE FOLLOWING QUESTIONS (40 points)、1. Compute the following expression:A: ⎰+∞∞-2(t 3+4) δ(1-t)dtB: {t[u(t)-u(t-2)]}’C: u(t)*u(t)2. Given a system y(t)=x 2(t),determine whether the continuous-time system iscausal or noncausal ,has memory or is memeoryless,is linear or nonlinear,istime invariant or time varying.Justify your answer.3. A linear time invariant system, when input 1x (t)=u(t), the response is-2t 1y (t)=(1-e )u(t), when input 2x (t)=cos(2t), the response is 2y (t)=cos(2t-/4)π, Findthe response when input the following signals.A: x(t)=u(t-1)+2cos(2t-4)B: x(t)=(t)+tu(t)δ4. Plot the magnitude function of the ideal lowpass filter ,if the input signal tothe i deal lowpass filte is δ(t) ,the response is y(t), the Fourier transform isY(ω),plot the |Y(ω)|.5. Compute the reverse transform of the following signals. A: 2s+2X(s)=s +7s+12B: -s 22se X(s)=(s+1)+1006. For the following linear time-invariant continuous-time systems, determine ifthe system is stable, marginally stable or unstable. A: 2s-4H(s)=s +7sB: -2t h(t)=e u(t) C: dy(t)-2y(t)=x(t)dt7. For the following ideal lowpass filter .the frequency response functionH(ω)=2[u(ω+π)-u(ω-π)]e -j3w .if x(t)=sin2t+pute the y(t).y (t )x (t )8. Plot the magnitude function of the ideal lowpass, ideal highpass, idealbandpass, ideal bandstop filter.三 、PART 3 COMPUTE AND ANSWER THE FOLLOWING QUESTIONS(35 points)1．Given an input of x(t)=4+2cos(10t+∏/4)+3 cos(30t+∏/2) .find the outputy(t) to each of the following filters.2．Given a bandlimited signal x(t) ,the Fourier transform X(ω) is shown in Fig. A. The system is shown in Fig. B.- Fig APlot the A(ω),B(ω) and Y(ω).{ Note: x(t)cos ω0t<--->1/2 [X(ω+ω0)+ X(ω-ω0)] }3. Given two signals x1(t)=x2(t) = compute theconvo lution y(t)=x1(t)*x2(t) and the Fourier transform Y(ω), plot the waveform of y(t) and |Y(ω)|.4．Given the frequency response function of the ideal lowpass filterH(ω)={ 1, |ω|<ωc and 0 ,|ω|>ωc } .the input signal x(t)=sinat/Пt. Compute and analyse the following questions.(a).if a < ωc,the filter output y(t).(b).if a > ωc,the filter output y(t).(c).which case come into being the output distortion.(where x(t)=sinat/Пt ---取样函数)5. For a linear time-invariant continuous-time system are connected as shown below. Compute the transfer function of the system and find theβ value if the system is stable2121,1,0{<≤-t t other all。