信号与系统 山大 2006 试卷.doc

Signals and Systems Test Paper BSchool of Electrical Engineering, 2004(Academic Year: 2006-2007, First Team) Student ID:_ Name:_PART 1 CHOOSING THE BEST ANSWER1. The following signals are shown below, the _is periodic signal.A. x(t)=sin2tU(t)B. xn=cos(/3)n+sin(/4)nC. xn=cos(1/4)n2. Suppose a linear time-invariant system，input x1(t)=cos4t the responds is y1(t)=0.5cos(4t-/6). If input x2(t)=4cos4t+2cos(4(t-2) then the response y2(t) is_ .A. 4cos(4t-/6)+2cos(4(t-2)- /6)B. 0.5cos(4t-/6) +2cos(4(t-2)- /6)C. 2cos(4t-/6)+cos(4(t-2)- /6)3. Given a linear time-invariant system , when input (t), the zero state response is e-tu(t), Then the system is_ . A. stableB. not stableC. marginally stable4. Suppose a linear time-invariant system, the unit pulse response is h(t). If input signal x(t), the response y(t)=x(t)*h(t) is _. A. zero input response of the systemB. zero state response of the systemC. complete response of the system 5. If X(s)= , the signal x(t) is_.A.B.C.6. Suppose that x(t) is given by x(t)=t t1tt2 and 1 tt2.The signal x(t) can be expressed _.A. x(t)=tu(t-t1)- u(t-t2)+ u(t-t1)- u(t-t2) B. x(t)=tu(t-t1)- u(t-t2)+ u(t-t2)C. x(t)=(t + 1)u(t-t1)- u(t-t2)7. The input/output relationship of the discrete-time system is given by yn=x2n. The system is _.A. linear, causal, time varying , memorylessB. nonlinear, causal, time varying, memoryC. nonlinear, causal, time invariant, memoryless8. The rectangular pulse train is periodic signal with fundamental period T. The amplitude spectrum is |Ck|. When T becomes large, Then_A. |Ck| becomes larger and the line spectrum interval (谱线间隔) becomes largerB. |Ck| becomes smaller and the line spectrum interval becomes larger C. |Ck| becomes smaller and the line spectrum interval becomes smaller9. If the poles of the transfer function of the system are located in the left-half open plane, then the system is _. A. stableB. not stableC. marginally stable10. The magnitude function of the ideal lowpass filter is 1 for |B, the time delay is td for all frequency. The input signal to the ideal lowpass filter is (t), the Fourier transform Y() of the response y(t) is _.A. 1, for all.B. ,for |BC. 1, for |BPART 2 ANSWER THE FOLLOWING QUESTIONS1. Compute the following expression:A: (t)cost dtB: tu(t)-u(t-2)C: (t)sin2t/t)dt2. A linear time-invariant continuous-time system are connected as shown below. The transfer functions of system 1 , system 2 and system 3 are Compute the transfer function H(s) of the overall system and unit impulse response h(t).3. For the following linear time-invariant continuous-time systems, determine whether the system is stable, marginally stable or unstable.A. H(s)=(s+1)/ (s+1)2+4B. H(s)=(s-4)/s(s+1)C. H(s)=1/s2(s+2)4. Suppose the Fourier transform of x(t) is X()，compute the Fourier transform of x(2t-5).5. The linear time-invariant continuous-time systems with differential equation y(t)+5y(t) =x(t)+3x(t). Compute the response y(t) resulting from x(t)=5, -t.6. A linear time-invariant discrete-time system has the unit pulse response .A. Compute the step response gn for n0.B. Compute the output response yn for n0 when input xn=un-un-5, no initial conditions.7. Given a signal x(t), the Laplace transform is X(s)=2se-s/(s+1)2+100, compute the signal x(t).8. Write the DTFT and N-point DFT expression of discrete-time signal xn,And point out the relationship between DTFT and DFT.PART 3 COMPUTE AND ANSWER THE FOLLOWING QUESTIONS1. Given signals x1(t) and x2(t), the waveform is shown below. Using graphic method (图解法)to compute the convolution y(t)=x1(t)*x2(t)。Plot the waveform of y(t)。2. Given a bandlimited signal x(t) ,the Fourier transform X() is shown in Fig. A. The system is shown in Fig. B.H()X() x(t) a(t) b(t) y(t) H() -10 0 10 cos30t cos30t 1 -15 0 15 Fig A Fig BPlot the A(),B() and Y(). Note: x(t)cos0t1/2 X(+0)+ X(-0) 3. The linear time-invariant continuous-time syst