信号与系统习题集

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 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 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 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(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. The 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) = ( ).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) = , 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 . And 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 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 differential 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 continuous-time LTI system. The unit impulse +-response h(t) satisfies ( ).A. B. C. D. 13. The input-output relationship of a causal 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 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) = 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.Figure 65. Let and , as illustrated in the Figure 6.(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)?6. Let Show that for 0 t 0, 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 function 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 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 ( ).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 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 impulse response of 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 a causal signal x(t) is , then x(t) = ( ).A. B. C. D. 11. A continuous-time LTI system can be described by its system function H(s), and it is known that the frequency response H(j) exists, then the system must be ( ).A. time-invariant B. causal C. stable D. linear12. Let , then the Laplace transform of y(t) is Y(s) = ( ).A. B. C. D. 13. Let be the Laplace transform of signal x(t), then ( ).A. B. C. D. 14. Let X(s) denote the Laplace transform of x(t), then the Laplace transform of signal x(2t - 5) is ( ).A. B. C. D.15. H(s) is the system function of an LTI system, then mathematical form of the unit impulse response h(t) can only be determined by ( ).A. the zeros of B. the poles of C. the input signal D. the input signal and the poles of 三、综合题(分析、计算)1. Given a causal LTI system, if the input signal is , the output response is , (1). Determine the system function H(s);(2). Is the system stable? Why?(3). If we apply the signal to the system, determine the corresponding output response y(t).2. Consider a causal LTI system described by the differential equation: (1). Determine the system function H(s);(2). Plot the pole-zero diagram.(3). Is the system stable? Why?(4). If we apply the signal to the system, determine the corresponding output response y(t).3. It is known that is the Laplace transform of a continuous-time signal x(t). Determine the inverse Laplace transforms for each of the following ROCs:(1). Res -1;(2). -2 Res -1;(3). Res -2.4. Let be the Laplace transform of signal x(t). Determine all possible expressions of x(t) corresponding to X(s) using the partial-fraction expansion technique.5. It is known that the system function of an LTI system is , and , where, h(t) and g(t) are the unit impulse and unit step responses of the system. Determine the unit step respons