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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 % 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（ ）. (a) X1??j??e?3j? (b) X1?j??e3j? (c) X1?j??e?3j? (d) X1??j??e3j?
1x1?t?1x2?t?0?112t0?1123tFigure 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 ( ). (a) finite duration (b) right-sided (c) left-sided (d) two sided
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 （ ）. 2dtdt(a) Low-pass filter (b) Band-pass filter (c) High-pass filter (d) Band-stop filter 5.The Fourier transform of the signal x?t? is shown in Figure 2.The signal x?t? may be (a) real and even (b) real and odd
(c) pure imaginary and odd (d) pure imaginary and even
6. The Laplace Transform of
X?j??1?2?10?1Figure 2
12?f(t)?tu(t?1) is F(s)?（ ）.
(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第 1 页 共 6 页
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二、计算题（ 共70分）
得 分 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???????/T .Deduce the value of ?M so that Y(j?)?0 for ???M.Specify the range
?0,???/Tof values for the sampling period T which ensures that yr?t?=y?t?.
第 2 页 共 6 页
y?t?yp?t?yr?t?Figure 3
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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，where is the unit step function. u??x?t??u?cos(?t)?????0,??0(a) Sketchx?t?. (b) Determine the magnitude and phase response of this system. (c) Determine the output y?t?.
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3（17分）A causal continuous-time LTI system is given in Figure 4.
(a)Determine the range of the constant K to ensure that the system is stable. (b)If K=2, determine the unit step responses?t?.
x?t?得 分
1/S 1/S y?t?－3 －2 K Figure 4
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4（20 分）Suppose that we are given the following information about a causal discrete-time LTI system:
（1）If the input is x?n??u?n?，then the output is y?n??a?1/2?u?n??2?1/3?u?n?. （2）The value of the unit impulse response at n=0 is h?0??1. Solve the following problems：
(a) Determine the system function H?z?，and indicate its ROC. (b) Draw a block diagram representation of this system. (c) Determine the unit impulse response h?n?.
(d) Supposeg[n]??nh?n?. Determine the range of real number?so that g[n] is the unit impulse response of a stable system.
nn得 分 第 5 页 共 6 页
【优质】电子科技大学 第 1 学期信号与系统期 末 考试 A 卷
