全国2008年4月自考信号与系统真题课程代码：02354一、单项选择题（本大题共12小题，每小题2分，共24分）在每小题列出的四个备选项中只有一个是符合题目要求的，请将其代码填写在题后的括号内。
错选、多选或未选均无分。
1．RLC 串联电路发生谐振的条件是（ ）A ．LC10=ω B ．LC πω210=C ．LC f 10=D ．LCR=0ω2．已知信号)(t f 的波形如题2图所示,则)()1(t t f ε-的表达式为（ ）A ．)3(-t εB ．)3()(--t t εεC ．)(t εD ．)3()(+-t t εε 3．计算⎰∞∞-=-dt t t )6(sin 2πδ（ ） A ．1 B ．1/6C ．1/8D ．1/44．已知⎰∞-=t d t f ττδ)()(,则其频谱=)(ωj F （ ）A ．ωj 1B ．j ωC ．)(1ωπδω+j D ．)(1ωπδω+-j 5．信号)(1t f 与)(2t f 的波形分别如题5图(a ),(b )所示,则信号)(2t f 的频带宽度是信号)(1t f 的频带宽度的（ ）A ．2倍B ．1/2倍C ．1倍D ．4倍6．已知某周期电流t t t i 5sin 223sin 221)(++=,则该电流信号的有效值I 为（ ） A ．3A B ．1A C ．17A D ．10A 7．已知)(t f 的拉普拉斯变换为F (s ),⎰-∞-0)(dt t f 有界,则⎰∞-td f ττ)(的拉普拉斯变换为（ ）A ．)(1s F sB ．)0()(1--f s F sC ．⎰-∞-+0)(1)(1ττd f ss F sD ．⎰-∞--0)(1)(1ττd f s s F s8．已知)(t f 的拉普拉斯变换为F (s ),且F (0)=1,则⎰∞-0)(dt t f 为（ ）A ．π4B ．π2C ．π21D ．19．系统函数22)()(c a s bs s H +-+=,a ,b ,c 为实常数,则该系统稳定的条件是（ ）A ．a <0B ．a>0C ．a=0D ．c =010．已知某离散序列)(n f 如题10图所示,则该序列的数学表达式为（ ） A ．)1()1()(+-=n n f n ε B ．)1()1()(--=n n f n ε C ．)()1()(n n f n ε-=D ．n n f )1()(-=11．已知某系统的差分方程为)1()()2()1()(0101-+=-+-+n f b n f b n y a n y a n y ,则该系统的系统函数H (z )为（ ）A ．201011)(z a z a zb b z H +++= B ．211011)(1---+++=z a z a z b b z HC ．102120)(a z a z z b z b z H +++=D ．20111011)(---+++=z a z a z b b z H12．已知)1(3)(+=z zz F ,则)(n f 为（ ）A ．)()3(n n ε-B ．)()1(31n n ε-C ．)(31n nε⎪⎭⎫⎝⎛ D ．)(3n n ε二、填空题（本大题共12小题，每小题2分，共24分） 请在每小题的空格中填上正确答案。
TEST OF HUAZHONG UNIVERSITY OF SCIENCE & TECHNOLOGY (A)Course: SIGNALS & SYSTEMS (Closed Book) (2008/05/24)SPECIALTY_________CLASS_________NAME__________No.____________1. (20 points)Consider the following problems, then fill in the blanks. (2 points for each blank)(a)()()=-⎰-dt t t 3sin 2πππδ__________________;(b) The fundamental period of sequence ⎪⎭⎫ ⎝⎛+=376cos ][n n x π is________________; (c) If a continuous-time system is defined by ()()t x e t y t -=1, then we can determine that it ’s a (linear / nonlinear) _____________, (time invariant / time variant) _________________, (causal / noncausal) _____________ system;(d) Consider a discrete-time system with the input and output relationship being[][][2]y n x n x n =-, if the input [][]n A n x δ=, here A is an arbitrary real or complex number,the output []y n =___________;(e) If an LTI system with impulse response ()t h 1 is invertible, and its inverse system has an impulse response ()t h 2, then we have 12()()h t h t *=______________;(f) The constant component of the continuous-time periodic signal ()sin()x t t ω= is________; (g) A signal ()x t with Fourier transform ()ωj X undergoes impulse-train sampling. If()0=ωj X for s rad /105>ω, then the Nyquist sampling period is___________ second ; (h) Consider a signal ()t x 1 with FT ()ωj X 1. If ()01=ωj X for m ωω>, then forsignal ()⎪⎭⎫ ⎝⎛=2312t x t x with FT ()ωj X 2, there must be ()02=ωj X for >ω_________.2．(10 points) ()t x is shown in Figure 1, sketch and label carefully the signals ()ττd x t⎰∞--2and ⎥⎦⎤⎢⎣⎡⎪⎭⎫ ⎝⎛+12t x dt d .Figure 13. (8 points) Verify that if the input signal []x n to an LTI system is periodic with period N , then the output []y n is also a periodic signal with the same period.4. (10 points)(a) Evaluate the Laplace transform of signal 2()tx t t e -= and specify its ROC.(b) Evaluate the inverse z-transform of ()a z z a z X >⎪⎭⎫ ⎝⎛+=1ln .5. (10 points) Consider the discrete-time periodic sequence [][4]k x n n k δ∞=-∞=-∑, determine itsFourier series coefficients k a and its Fourier transform, and plot []x n and ()j X e ω.6. (10 points) Consider an ideal low-pass filter with frequency response 1,()0,ccH j ωωωωω⎧<⎪=⎨>⎪⎩.Suppose that the input signal sin()()at x t tπ=, please answer the following questions: (a) Determine the output ()y t in the case of c a ω<; (b) Determine the output ()y t in the case of c a ω>; (c) In which case, the input signal is not distorted? And evaluate 2()y t dt ∞-∞⎰in thiscase.7. (16 points) Suppose we are given the following information about a causal LTI system described by a linear constant-coefficient second-order differential equation with impulse response ()h t and system function ()H s : 1. If ()1x t =, then ()1y t =-; 2. ()H s has a pole at1s =-and a zero at 1s =; 3. ()h t doesn’t contain any impulse s and ()20=+h . Try to answer the following questions: (a) Determine the differential equation and draw a direct-form block diagram for the system; (b) Is the system stable? (c) Determine the output of the system when the input ()()x t u t =and the initial conditions (0)4,(0)3y y --'=-=.8. (16 points) A discrete-time causal system with system function 1()H z depicted in Figure 2(a), (a) If the system 1()H z is cascaded with another causal system with system function 2()H z to construct a system with system function ()a H z , just as Figure 2(b) shown, to make21()10.25j a j H e eωω-=-, determine 2()H z ; (b) Determine the unit sample response []a h n of the system ()a H z ; (c) Let ()b H z be the system function of a causal system shown in Figure 2(c), to make ()()ωωj a j b e H e H =, determine the values of 1b 、2b 、3b in Figure 2(c); (d) Write]n[]x n[]x n[]n a[]x n []y n(c)Figure 2。
华南理工大学管理学考研历年真题与答案目录Ⅰ编写说明 2Ⅱ使用说明 3Ⅲ考试题型解读 4一、学院专业考试概况 4二、考试题型深入剖析及对应高分解题技巧 8三、2014年真题解读 9四、2015年考试展望 9五、高分复习方略 9六、章节考点分布表 13Ⅳ近年真题与答案详解 17824华南理工大学2008年攻读硕士学位研究生入学考试试卷 17824华南理工大学2009年攻读硕士学位研究生入学考试试卷 22824华南理工大学2010年攻读硕士学位研究生入学考试试卷 27824华南理工大学2011年攻读硕士学位研究生入学考试试卷 33824华南理工大学2012年攻读硕士学位研究生入学考试试卷 36824华南理工大学2013年攻读硕士学位研究生入学考试试卷 41824华南理工大学2014年攻读硕士学位研究生入学考试试卷 45824华南理工大学2008年攻读硕士学位研究生入学考试答案详解 48 824华南理工大学2009年攻读硕士学位研究生入学考试答案详解 61 824华南理工大学2010年攻读硕士学位研究生入学考试答案详解 75 824华南理工大学2011年攻读硕士学位研究生入学考试答案详解 89 824华南理工大学2012年攻读硕士学位研究生入学考试答案详解 99 824华南理工大学2013年攻读硕士学位研究生入学考试答案详解 113 824华南理工大学2014年攻读硕士学位研究生入学考试答案详解 126Ⅴ高分备考指导 117一、高分备考方略 117（一）考研英语 117（二）考研政治 121（三）考研专业课 125二、辅导班推介 127（一）公共课 127（二）专业课 130三、教材与辅导书推介 132华南理工大学题型分析部分内容摘要……绝大部分的专业在研究生考试的初试专业考试的科目为信号与系统，使用的教材有两本： 1.《信号与系统》[美]ALAN.OPPENHEIM,ALANS.WILLSKY,刘树棠译,西安交通大学出版社1998.3(第二版);2.《Signals and Systems》(Second Edition)[美] Alan V.Oppengeim,AlanS.Willsky,S.Hamid Nawab,电子工业出版。
