华中师范大学信号与系统期末考试(A卷)2016-2017

1、华中师范大学2016-2017学年第二学期期末考试试卷（A卷）得分评阅人answer)课程名称信号与系统课程编号21110014 任课教师罗小巧胡君红题型选择题填空题画图题计算题总分分分I.选择题 Choice (每个选项 3 分 3 points for each correct1 .判断系统特性：y（t）="- D,和阳分别表示系统的输入和输出。（）Detennine the properties of the system: y (t) =- 1),denotes the system outputand x(t) is the system inpu

2、t.A 线性、稳定 linear, stableB 线性、因果、不稳定 linear, causal, unstableC 线性、时变、稳定 linear, time variant, stableD 线性、时不变、因果、不稳定 linear, time invariimt, causal, unstable2 ,下列各表达式中错误的是oWhich of the following expressions is wrong?A if y(t)=x(t)*h(t), then y(-t)=x(-t)*h(-t) B if y(t)=x(t)*h(t), then y(2t)=x(2t)*h(2t

3、)c if y(t)=x(t)*h(t),then 幽=蛆 * 力=%2 * *&)D x(t)*y(t)+z(t)=x(t)*y(t)+x(t)* z(t) dt dtdt3 .线性时不变系统的单位冲激响应扭£)=%(£ - 2),判断系统的性质。()The impulse responses of continuous-time LTI systems is 力(亡)=eu(t - 2) .Determine the properties of the system.A 因果、稳定 causal, stableB 非因果、不稳定 not causal, unst

4、ableC 非因果、稳定 not causal, stable D 因果、不稳定 causal, unstable4 .一个连续时间周期信号，其傅里叶级数表示为大七)=fcos(Qr)J强，该信号是()女一70Consider the continuous-time periodic signal whose Fourier series representation is 8jktx(t) = 2 cos (Me ° , what is the signal ?A不是实值函数not realB 实奇函数real and oddC 实偶函数 real and evenD 不能确定 c

5、annot be ascertained5 .如果/")的傅里叶变换是尸(/，则/可-3)的傅里叶变换是( )oF(J is the Fourier traiisfonn of f (/), which of the following is the Fourier transfonnA /b F(jco)e-3ja C /川D F(j36 .有多少个信号在其收敛域内都有如下所示的拉普拉斯变换()How many signals have a Laplace transform that may be expressed as below?(s-l)(s + 2)(s + 3)(s2

6、 + s + 1)B 3个 C4个 D 5个得分评阅人II.填空题 Fill in the blanks (每空 3 分 3 points for each coirect answer)1 .一个连续时间线性系统S的输入为多=对应的输出为k=/巴输入为 *2-)=，兀'，对应的输出为匕=/"，若输入/(£)= cos(2t),求系统S的输出 力=。A continuous-time linear system S with input x(t) and output y(t) yields the following input-output pairs:*i(&

7、#163;)= ej2z >y/t)=夕"，*式2)= f y2(?) =Ifxt) = cos (2t), detennine the corresponding output y3(t) = .2 .求积分，cos (2;rt)演2 + 3)dt =。Evaluate the integral j cos+ 3)c/t = .HG) =H(s) of this system is3 ,设占为连续时间周期信号，其基波频率为例，傅里叶系数为名，已知 均=占(1 -,)+ xSt -1),利用a*导出信号沟的傅里叶级数系数 4 =2Let 占(£)be a contin

8、uous-time periodic signal with fundamental frequency 例 and Fourier coefficient ak . Given that x2(t) =- t) + 占9 - 1), the Fourier series coefficient bk of signalx2(t) in terms of ak is .4 .已知x(f)的傅里叶变换为才(加)，求xG - 1)的傅里叶变换为。drConsider the Fourier transform of x(Z) is X (, the Fourier transfomi of pr

9、- 1) is5 .考虑一个线性时不变系统，其单位冲激响应为方9)=显沙，求该系统对输入信号 ntx(£)= cos (6匕)的输出 y(t) =。sin (4t)Consider an LTI system with impulse response /?(f)= ，the output y(t) of the systemntfor input x(t) = cos (6t) is .6 .设x(/)是一个奈奎斯特率为4的信号，试确定信号V。)的奈奎斯特率 oLet x(t) be a signal with Nyquist rate %, the Nyquist rate fo

10、r a 2 (f) is .7 .设/?(/) = %(/)-9即(T),其拉普拉斯变换的收敛域为。Let, the region of convergence for Laplace transform is8有一因果线性时不变系统，其方框图如图1所示，试确定描述该系统的系统函数A causal LTI system has the block diagram representation as shown figure 1. The system function图 1 Figure 1得分评阅人III.绘图题 Drawing (16 points )1 .(8分)根据相应的零极点图，利川

11、傅立叶变换模的几何求值方法，画出下列拉普拉斯变换其相应的傅立叶变换的模特性，并确定其模特性是否近似为低通、高通或带通滤波器?(8 points) Using geometric evaluation of the magnitude of the Fourier transfonn from the corresponding pole-zero plot, sketch the graph of the magnitude of the Fourier transfonn for the following Laplace transform .Detennine whether the m

12、agnitude of the corresponding Fourier transfonn is approximately lowpass, highpass, or bandpass filter.4(s) = -,Res > -3s + 32 .(8分)假设X(t)的傅里叶变换X(j0) = 0,心| > 3”,而信号g可用x表示成:g(t) = x(t) cos cot - < (x(t)cos cot *sin aJ、7lt ,其中*表示卷积，且小> Gm。试根据x(t)的频谱X(j画出g(t)的频谱G(j(D), X(j如图2所示。(8 points)

13、Assure that x(t) is a signal whose Fourier transform X(jOO) is zero for |o)| >signal g(t)may be expressed in tenns of x(t) as = x(r)COs -cos w) *sin工ntwhere * denotesconvolution and (ji)c > 60.Sketch the spectrum G(jCO)of g(t) in terms of the spectrum X(j(O)ofx(t). X(jO) is shown as figure 2.图

14、 2 Figure 2得分评阅人IV.1.( 10 分)假设-Y(t)= <计算题 Problem Solving (42points)1,0,0 < <其他1，且 h(t) = x(2t),求出并画出 y(t) = x(t)*h(t)o(10 points) Suppose that x(t)=1 ,10,0 - r 1 and h(t) = x(2t). Determine and elsewhere2. ( 10分)一个线性时不变系统其输入及响应分别为M，) = "T +G”， 的=23-2”),(1)求该系统的频率响应；(2)确定该系统的单位冲激响应；(3)

15、求出联系输出与输入的微分方程。(10 points) Consider an LTI system whose response to the signal x(r) =+ e"' (1) is thesignal y(r) =- 2er u(t).(1) Detennine the frequency response of the system;(2) Detennine the impulse response of the system;(3) Give the differential equation relating the input and die outp

16、ut of the system.3"。分）在图3所示系统中，输入信号f由一冲激串州采样。设f=¥，sill - ts(t) = W f) = V 咏 一 nT), T=2s , h(t)=-一匚，确定输出 y(t)c(10 points) Shown in Figure 3 is a system in which the input signal is multiplied by a periodic impulse train. We aresin jt eiven the following infomiation: f(t)=JJ7CtHX,s(t)=乡(t) =

17、 2- /)，T=2s , and the impulser=-xsint response of the subsystem is h(t) = .Determine the output y(t).Ttt/IX7 2 /(4. (12分)有一个稳定的连续时间线性时不变系统，其系统函数H(s)是有理的，零极点图如图4所示，输入x") = 3时对应的输出y(t) = -lo确定系统函数H (s)及其收敛域。(b)确定系统的单位冲激响应h(t),该系统是因果的吗？输入X”)= /”)，求输出了。(12points) Consider a stable LTI system with rational system function H(s) for which the pole-zero plot is shown in Figure 4. If