信号与系统习题集(3)

1、信号与系统练习题集第一部分：信号与系统的时域分析一、填空题1. ( ).2. The unit step response is the zero-state response when the input signal is ( ).3. Given two continuous time signals x(t) and h(t), if their convolution is denoted by y(t), then the convolution of and is ( ).4. The convolution ( ).5. The unit impulse response is

2、 the zero-state response when the input signal is ( ).6. A continuous time LTI system is stable if its unit impulse response satisfies the condition: ( ) .7. A continuous time LTI system can be completely determined by its ( ).8. ( ).9. Given two sequences and , their convolution ( ).10. Given three

3、 LTI systems S1, S2 and S3, their unit impulse responses are , and respectively. Now, construct an LTI system S using these three systems: S1 parallel interconnected by S2, then series interconnected by S3. the unit impulse response of the system S is ( ).11. It is known that the zero-stat response

4、of a system to the input signal x(t) is , then the unit impulse response h(t) is ( ).12. The complete response of an LTI system can be expressed as a sum of its zero-state response and its ( ) response.13. It is known that the unit step response of an LTI system is , then the unit impulse response h

5、(t) is ( ).14. ( ).15. We can build a continuous-time LTI system using the following three basic operations: ( ) , ( ), and ( ).16. The zero-state response of an LTI system to the input signal is , where s(t) is the unit step response of the system, then the unit impulse response is h(t) = ( ).17. T

6、he block diagram of a continuous-time LTI system is illustrated in the following figure. The differential equation describing the input-output relationship of the system is ( ).+-+2318. The relationship between the unit impulse response h(t) and unit step response s(t) is s(t) = ( ), or h(t) = ( ).1

7、9. If the unit impulse response h(t) of 二、选择题1. For each of the following equations, ( ) is true.A、 B、 C、 D、2. Given two continuous-time signals and , if the convolution of and is denoted by , then the convolution of signals and is ( ).A. B. C. D. 3. The unit impulse response of an LTI system is h(t

8、) = , this system is ( ). A. causal and stable B. causal and unstable C. noncausal and unstable D. noncausal and stable4. = ( ). A. 1 B. 3 C. 9 D. 05. For an LTI system, if the input signal is , the corresponding output response is , if the input signal is , the corresponding output response is . An

9、d if the input signal is , the corresponding output response is ( a and b are arbitrary real numbers ). Then the system is a ( ) system. A. linear B. causal C. nonlinear D. time invariant6. = ( ).A. B. C. D. 7. ( ). A. B. C. D. 8. Given two sequences and , their lengths are M and N respectively. The

10、 length of the convolution of and is ( ).A B C D9. The unit impulse response of a continuous-time LTI system is , the differential equation describing the input-output relation of this system is ( ).A. B. C. D. 10. The input-output relation of a continuous-time LTI system is described by the differe

11、ntial equation: . The unit impulse response of the system h(t) ( ).A . does not include B. includes C. includes D. is uncertain11. Signals and are shown in the following figures. The expression of the convolution is ( ).-1110-11(1)0(1)A. B. C. D. 12. The following block diagram represents a continuo

12、us-time LTI system. The unit impulse +-response h(t) satisfies ( ).A. B. C. D. 13. The input-output relationship of a continuous-time system is described by the differential equation: , then the unit step response ( ).A. B. C. D. 三、综合题（分析、计算题）1. The input-output relationship of a continuous-time LTI

13、 system is described by the equation: ，a. Determine the unit impulse response h(t) of the system.b. Determine the system response y(t) to the input signal .Figure 22. Given an LTI system depicted in Figure 2. Assume that the impulse response of the LTI system is h(t) = e-tu(t), the input signal x(t)

14、 = u(t) - u(t-2). Determine and sketch the output response y(t) of the system by evaluating the convolution y(t) = x(t)*h(t).3. Remember the following identities: 4. Consider an LTI system S and a signal . Ifand ,determine the impulse response h(t) of S.5. Let and .(a). Compute y(t) = x(t)*h(t).(b).

15、 Compute g(t) = dx(t)/dt * h(t).(c). How is g(t) related to y(t)?Figure 66. Let and , as illustrated in the following figure.(a). Compute y(t) = x(t)*h(t).(b). Compute g(t) = dx(t)/dt * h(t).(c). How is g(t) related to y(t)?7. Let Show that for 0 t < 3, and determine the value A.8. A causal LTI s

16、ystem is described by the differential equation:If the input signal is , determine the zero-state response y(t) of the system.9. In this problem, we illustrate one of the most important consequences of the properties of linearity and time invariance. Specifically, once we know the response of a line

17、ar system or a linear time-invariant system to a single input or responses to several inputs, we can directly compute the responses to many other input signals. Figure 9(a)(b)(c)(d)(a). Consider an LTI system whose response to the signal x1(t) in Figure 9(a) is the signal y1(t) illustrated in Figure

18、 9(b). Determine and sketch carefully the response of the system to the input x2(t) depicted in Figure 9(c).(b). Determine and sketch the response of the system considered in part (a) to the input x3(t) shown in Figure 9(d).第二部分：信号与系统的频域分析一、填空题1. The frequency response of an ideal filter is given by

19、 ， if the input signal is , the corresponding output response y(t) = ( ).2. The Fourier transform of signal is ( ).3. The Fourier transform of signal is ( ).4. Assume that the Fourier transform of is denoted as , then the Fourier transform of is = ( ).5. The Fourier transform of a continuous time pe

20、riodic signal is = ( ).6. It is known that the Fourier transform of is , then the Fourier transform of is ( ).7. The Fourier transform of signal is denoted as , the Fourier transform of is ( ).8. A time shifting leads to a ( ).9. The frequency responses of two LTI systems are assumed to be and , the

21、 frequency response of the interconnection of cascaded by is = ( ).10. A time-domain compression corresponds to a frequency-domain ( ).11. For a signal x(t), if the condition is satisfied, then the Fourier transform of x(t) exists, this condition is ( ) but not ( ).12. Figure 12 shows a continuous-t

22、ime signal , its Fourier transform is denoted as , then ( ). (Without evaluating).-1110Figure 1213. For a continuous-time LTI system, if the zero-state response of the system to the input signal is , then the frequency response of the system is ( ).14. The Fourier transform of signal is ( ).15. The

23、inverse Fourier transform of is ( ).16. The frequency spectrum includes two parts, one is ( ), the other is ( ).17. Let denote the Fourier transform of signal , then the Fourier transform of signal is ( ). (Expressed using ).18. Let denote the Fourier transform of signal , then the Fourier transform

24、 of signal is ( ). (Expressed using ).19. The period of the periodic square wave increases, the space of the spectral lines ( ).20. Consider a continuous-time ideal lowpass filter S whose frequency response is When the input to this filter is a signal x(t) with fundamental period T = /6 and Fourier

25、series coefficients ak, it is found that For k is ( ) it guaranteed that ak = 0.21. Consider a continuous-time LTI system whose frequency response is If the input to this system is a periodic signal with period T = 8, the corresponding system output is y(t) = ( ).二、选择题1. The frequency response of an

26、 ideal lowpass filter is . If the input signal is , the output response is = ( ).A. B. C. D. 2. The Fourier transform of the rectangular pulse is ( ).A. B. C. D. 3. Let denote the Fourier transform of signal , the Fourier transform of is ( ).A. B. C. D. 4. Let denote the Fourier transform of signal

27、, the Fourier transform of is ( ).A. B. C. D.5. The Fourier transform of the rectangular pulse is ( ).A. B. C. D. 6. The condition for signal transmission with no distortion is ( ). A. The magnitude response is a constant in the passband.B. The phase response is a line cross the origin in the passba

28、nd.C. The magnitude response is a constant and the phase response is a line cross the origin in the passband.D. The phase response is constant and the magnitude response is a line cross the origin.7. The bandwidth of signal is 20KHz, the bandwidth of signal is ( ).A.20KHz B.40KHz C.10KHz D.30KHz8. L

29、et denote the Fourier transform of signal , the Fourier transform of is ( ).A.B. C. D. 9. Let denote the Fourier transform of signal , the Fourier transform of is ( ).A. B. C. D. 10. Let denote the Fourier transform of signal, then ( ).A. 2 B. C. D. 411. Let denote the Fourier transform of signal ,

30、the Fourier transform of is ( ).A B C D12. Let denote the Fourier transform of signal , the Fourier transform of is ( ).A. B. C. D. 13. The Fourier transform of signal is ( ).A. B. C. D. 14. Let and . The Fourier transform of y(t) is ( ).A. B. C. D. 15. Consider the square wave , as decreases, the w

31、idth of the main lobe of ( ).A. increases B. decreases C. does not change D. can not be determined 16. It is known that the bandwidth of x(t) is, the bandwidth of is ( ).A. B. C. D. 17. The inverse Fourier transform of is ( ).A. B. C. D. 18. The Fourier transform of signal is , then the Fourier tran

32、sform of signal is ( ).A. B. C. D. 19. Given an LTI system with its frequency response , it is known that the Fourier transform of the output response y(t) is , the input signal =( ).A. B. C. D. 20. The frequency response of an ideal lowpass filter is , its unit impulse response is h(t) = ( ).A. B.

33、C. D. 三、综合题(分析、计算)1. Consider a continuous-time LTI system whose frequency response is If the input to this system is a periodic signal with period T = 8, determine the corresponding system output y(t).Figure 22. The fundamental period of a continuous-time periodic signal is 0 = , Figure 2 shows the

34、 spectral coefficients of x(t). (a) Write out the expression of x(t).(b) If x(t) is applied to an ideal highpass filter with frequency response , determine the output signal y(t).3. Figure 3.a illustrates a communication system. Let X1(j) and X2(j) denote the Fourier transforms of x1(t) and x2(t), r

35、espectively. It is known that 1 = 4, 2 = 8, and the frequency response of the ideal bandpass filter is H1(j), the overall output response is y(t). In order to get y(t) = x1(t):(1). Plot the magnitude of the Fourier transform W(j) of w(t). (2). Choose an appropriate frequency 3.(3). Plot the magnitud

36、e responses of H1(j) and H2(j).Figure 3 (a)(b)Figure 44. Figure 4 shows the Fourier transform of a periodic continuous-time signal .(1). Write out the expression of .(2). Let be the frequency response of an ideal lowpass filter, and is applied to the filter, determine the output response y(t) of the

37、 filter.。5. For a causal LTI system, the input and output signals are , , respectively.(1). Determine the frequency response .(2). Determine the unit impulse response .(3). Determine the differential equation describing the input-output relationship of the system.6. The frequency response of an idea

38、l bandpass filter is , the unit impulse response is denoted as h(t), we now have that , determine .7. A continuous-time signal is sampled by the impulse train getting , where, = 0.5s.(1). Plot the Fourier transform of .(2). Plot the Fourier transform of .(3). Let be the frequency response of an idea

39、l bandpass filter. If is applied to the filter, the output response is denoted as y(t), plot the Fourier transform of y(t).(4). By observing, write out the expression of .图48. Figure 8 illustrates a communication system, The Fourier transforms of the input and output signals and are denoted as and ,

40、 respectively. If x(t) = cos(0.5t), determine y(t) and plot .Figure 89. Let X(j) denote the Fourier transform of the signal x(t) depicted in Figure P4.25.Figure P4.25.a.(a). Find .(b). Find .(c). Evaluate .(d). Evaluate .(e). Evaluate .(f). Sketch the inverse Fourier transform of Re X(j).Note: You s

41、hould perform all these calculations without explicitly evaluating X(j).10. Consider an LTI system whose response to the inputis (a). Find the frequency response of this system.(b). Determine the systems impulse response.(c). Find the differential equation relating the input and the output of this s

42、ystem.11. Let Assuming that x(t) is real and X(j) = 0 for | 1, show that there exists an LTI system S such that x(t)g(t).第三部分：信号与系统的s域分析一、填空题1. The ROC of the Laplace transform is , then the inverse transform is = ( ).2. It is known that the LTI system described by is stable, then the ROC of H(s) is

43、 ( ).3. The system function of a causal LTI system is , then the differential equation describing the input-output relationship of the system is ( ).4. The Laplace transform of signal is ( ), the associated ROC is ( ).5. Assume that the system function of an anticausal LTI system is , then the frequ

44、ency response ( ), the unit impulse response ( ).6. It is known that a causal continuous-time LTI system H(s) is stable, then all poles of H(s) are located in ( ).7. It is known that the Laplace transform of signal x(t) is , then ( ).8. The differential equation describes the input-output relationsh

45、ip of an LTI system, then the system function is H(s) = ( ).9. The Laplace transform of a causal signal x(t) is denoted as X(s), then the Laplace transform of signal is ( ).10. Given a continuous-time LTI system, it is known that the zero-state response to arbitrary input x(t) is x(t-t0), t0 > 0,

46、 then the system function of the system is H(s) = ( ).11. The Laplace transform of a continuous-time signal x(t) is , then x(t) = ( ).12. Figure 1.12 illustrates an LTI system, its system function is H(s) = ( ).+-+23Figure 1.1213. It is known that a causal continuous-time LTI system with system func

47、tion is stable, then the coefficient a must satisfy: ( ).14. Given two signals and , and , then the Laplace transform of y(t) is Y(s) = ( ).15. A causal continuous-time LTI system has rational system function H(s). The sufficient and necessary condition for which the system is stable is that all of

48、the poles of H(s) are located in the ( ) of the s-plane.二、选择题1. The Laplace transform of signal is ( ).A. B. C. D. 2. The system function H(s) of an LTI system has two poles at p1 = -3, p2 = -1, and one zero at z = -2 in the finite s-plane. It is known that H(0) = 2, then the system function is ( ).

49、A. B. C. D. 3. The Laplace transform of signal is , then the ROC of X(s) is ( ).A. B. C. D. 4. Let with its ROC: , then the inverse Laplace transform is x(t) = ( ).A. B. C. D. 5. The system function of an LTI system is , then the system is ( ).A. causal and stableB. causal and unstableC. anticausal

50、and stableD. anticausal and unstable6. The Laplace transform of signal is , then the ROC of X(s) is ( ).A. B. C. D. 7. The system function of an LTI system is, then the system is ( ).A. B. C. D. 8. The system function of a causal LTI system is , then the system is ( ).A. stableB. unstableC. critical stable (临界稳定)D. indeterminacy9. The unit step response of a continuous-time LTI system is then the system function of the system is H(s) = ( ).ABCD10. The Laplace transform of x(t) is , then x(t) = ( ).A. B. C. D. 11. A continuous-time LTI system can be