电子科技大学 学年第 学期信号与系统期 末 考试 A 卷

电子科技大学2014-2015 学年第 1 学期期 末 考试 A 卷

课程名称： 信号与系统 考试形式： 一页纸开卷 考试日期： 20 15 年 1 月 15 日 考试时长： 120 分钟 课程成绩构成：平时 10 %， 半期考试 20 %， 实验 10 %， 期末 60 %文档收集自网络，仅用于个人学习 本试卷试题由 二 部分构成，共 5 页。

题号 一 1 得分 2 二 3 4 合计 得 分 一、选择填空题（共30分，共 6问，每问5分）

1. Consider two signals x1?t? and x2?t?, as shown in Figure 1. The Fourier transform of x1?t? is X1?j??. Then the Fourier transform

ofx2?t?should be（ ）.文档收集自网络，仅用于个人学习 (a) X1??j??e?3j? (b) X1?j??e3j? (c) X1?j??e?3j? (d) X1??j??e3j?

x1?t?x2?t?10112t0123t?1?1Figure 1 The waveforms of x1?t? and x2?t?

2. The convolution sum cos(?n)?{2nu?n?}?( ). (a)

1n112u?n?? (b) cos?n (c) cos??n?u?n?? (d) not existed 3333. Consider a stable discrete-time system, whose system function H?z? is a rational function and has only two poles：z1??1/2,z2?2. The positions of zeros are unknown. The impulse response h?n? of the system must be ( ).文档收集自网络，仅用于个人学习 (a) finite duration (b) right-sided (c) left-sided (d) two sided文档收集自网络，仅用于个人学习 4.The relation between the input and the output of a causal continuous-time LTI system is described by the differential equation

d2y?t?dy?t??3?2y?t??x?t?. The system is （ ）.文档收集自网络，仅用于个人学习 2dtdt(a) Low-pass filter (b) Band-pass filter (c) High-pass filter (d) Band-stop filter文档收集自网络，仅用于个人学习 5.The Fourier transform of the signal x?t? is shown in Figure 2.The signal x?t? may be文档收集自网络，仅用于个人学习 ?j??X1(a) real and even (b) real and odd

(c) pure imaginary and odd (d) pure imaginary and even文档收集自网络，仅用于个人学习

6. The Laplace Transform of

?2?1012??1f(t)?tu(t?1) is F(s)?（ ）.

Figure 2

(a)

1?s?s?s(1?e)1ee?s2(1?e)，Re[s]?0 (d) 2(1?s)，Re[s]?0 (1?s)s，Re[s]?0 (b) 2，Re[s]?0 (c) 2sss二、计算题（ 共70分）

得 分 1 / 5

1.（15 points）Suppose x1?t?and x2?t?are both band-limited signals, where X1?j???0 for ??200? ,

X2?j???0 for ??300?.Impulse-train sampling is performed on y?t??2x1?2t??3x2?t/3? to obtain yp?t??n????y?nT???t?nT?,

???T,as shown in Figure 3 where H?j?????0,???/T???/T .Deduce the value of ?M so that Y(j?)?0 for ???M.Specify the range

of values for the sampling period T which ensures that yr?t?=y?t?.文档收集自网络，仅用于个人学习 y?t?yp?t?yr?t?2 / 5

Figure 3

得 分 2.( 18 points ) Consider an LTI system with unit impulse response h?t??sin(1.5?(t?1))?sin(0.5?(t?1)).The input signal

?(t?1)?1,??0 is the unit step function.文档收集自网络，仅用于个人学习 x?t??u?cos(?t)?，where u??????0,??0(a) Sketchx?t?. (b) Determine the magnitude and phase response of this system. (c) Determine the output y?t?.文档收集自网络，仅用于个人学习

3 / 5

3（17分）A causal continuous-time LTI system is given in Figure 4. 文档收集自网络，仅用于个人学习 (a)Determine the range of the constant K to ensure that the system is stable.文档收集自网络，仅用于个人学习 得 分 (b)If K=2, determine the unit step responses?t?.文档收集自网络，仅用于个人学习 x?t?1/S －3 4 / 5

1/S －2 K Figure 4

y?t?