1、Signals&SystemsSecond Edition讲授者：电子工程学院讲授者：电子工程学院 孔斌孔斌课程说明课程说明参考书目参考书目:信号与系统分析信号与系统分析吕幼新吕幼新 张明友张明友 电子工业出版社电子工业出版社 信号与系统分析信号与系统分析闵大镒闵大镒 朱学勇朱学勇 电子科技大学出版社电子科技大学出版社课件下载课件下载:校园网校园网教师社区教师社区电子工程电子工程学院学院孔斌孔斌课件发布课件发布下载密码下载密码:2007Chapter 1 Signals and Systems 1.1 Basic Discrete-Time Signals 1.1.1 The Discrete
2、-Time Unit Impulse and Unit Step SequencesUnit Impulse n1n=020 n 0n01 nUnit Step u n1n 020 n 020 t 00 t1 tu t0 t 0 1dtt 001t dt du ttdt 2.Unit Impulse Function 0 t(1)t tu td 0 t积分区间积分区间 0u ttd 0 tt积分区间积分区间Chapter 1 Signals and Systems 1.2.2 The Properties of Unit Impulse Functions1.Sampling and Sift
3、ing propertiesIf f(t)is continuous at the point of t=0 tfttf0Sampling property 0fdtttfSifting propertyIn General 000tttftttf 00tfdttttf2.Scaling property3.If a is real,a 0 taat1Specially a=-1 tt Even functionChapter 1 Signals and Systems4.Properties of Unit Doublets（冲激偶的性质）（冲激偶的性质）3.Defining 01dttut
4、For any t 01tkkkkdttddttut 01dttu tutu11 ttutut0011Chapter 1 Signals and Systems 1.2.3 Continuous-Time Complex Exponential and Sinusoidal Signals stCetx t real is atCetx tjCetx0 t0sj Chapter 1 Signals and Systems General Complex Exponential Signals stx tCe0sjjCC e 1.3 Transformations of the independ
5、ent variable1.Time shift2.Time reversal3.Time-scaling4.Even and Odd Signals5.Differential and Integral Chapter 1 Signals and SystemsExample 1.1 Given the signal x(t)x(-3/2 t+1)0 1 2 t tx1Solution 1-1 0 1 t1tx1Time-shift-1 0 1 t1tx1Time-reversal-2/3 0 2/3 t12/3tx1Time-scalingSolution 2-2 -1 0 ttx 1Ti
6、me-reversal-4/3 -2/3 0 ttx2/31Time-scaling-2/3 0 2/3 t12/3tx1Time-shiftChapter 1 Signals and Systems信号的基本表示信号的基本表示-0 t tP2-0 ttu 0 ttu0 1 t 1 ttu1t0 1 t 0 t tu1-1 0 1 t1 tf-1 0 t1 11tut0 1 t 2 ttu20 1 2 t 1 11tutChapter 1 Signals and Systems信号的微分、积分运算信号的微分、积分运算Example 1.7 x(t)is depicted in Figure 1
7、.40(a),determinethe derivative of x(t).2 1 0 1 2 3 4 t-1x(t)0 1 2 3 4 t dttdx(2)(-3)(2)213224x tu tu tu t 213224dx ttttdtChapter 1 Signals and SystemsContinuous-Time System kkMkkkkNkkdttxdbdttyda00Discrete-Time System knxbknyaMkkNkk00N-order Linear Constant-coefficientDifferential Equation N-order L
8、inear Constant-coefficientDifference Equation 1.4 Continuous-time and discrete-time systemsChapter 1 Signals and Systems 1.4.1 Systems with and without Memory有记忆、无记忆系统有记忆、无记忆系统无记忆系统无记忆系统:在某时刻在某时刻(t)的输出仅仅与同时刻的输出仅仅与同时刻(t)的输入有关。的输入有关。memoryless（无记忆）（无记忆）identity system,memoryless 222nxnxny txty summer
9、kxnynk delay 1nxny integrate dxtytSystems with memoryChapter 1 Signals and Systems 1.4.2 Invertibility and Inverse Systems可逆系统与可逆性可逆系统与可逆性可逆系统可逆系统:不同的输入导致不同的输出（一一对应）。不同的输入导致不同的输出（一一对应）。System nx tx ty nyInverse System nxnw txtw tx txty2 ty txtw tytw21 kxnynk nx ny 1nynynw nxnw 0ny txty2noninvertible
10、 systems不可逆系统不可逆系统Chapter 1 Signals and Systems 1.4.3 Causality （因果性）（因果性）因果系统因果系统:在某时刻在某时刻(t)的输出只取决于同时刻的输出只取决于同时刻(t)或以前或以前(t)的输入。的输入。(与该时刻以后的输入无关）与该时刻以后的输入无关）Systems without memory 1y tx t ty txdCausal systems cos1y ttx tChapter 1 Signals and Systems非因果系统非因果系统:适用于非时间自变量信号的处理适用于非时间自变量信号的处理.knxMnyMMk
11、121 nxny txty2Not Causal 1.4.4 Stability （稳定性）（稳定性）Stable System y tB x tM ttxty txety not stable stableChapter 1 Signals and Systems 1.4.5 Time Invariance （时不变性）（时不变性）时不变系统时不变系统:系统参数不随时间改变系统参数不随时间改变(恒参系统恒参系统),系统的输出波系统的输出波形仅仅取决于输入波形形仅仅取决于输入波形,而与输入作用的时刻无关而与输入作用的时刻无关.txLtyIf 00ttyttxLTime invariant时不变
12、时不变 Consider a continuous-time system Delay t0 tx0ttxL0ttxL tx tyLDelay t00tty=time invariantsystem time-varyingsystemChapter 1 Signals and SystemsExample 1.14 txtysinDelay t0 tx0ttxL0sinttx txL txsinDelay t00sinttxEqual Time invariantExample 1.15 nnxnyNot equal Time-varyingDelay n0 nx0nnxL0nnnxL nx
13、 nnxnyDelay n000nnxnnChapter 1 Signals and SystemsExample 1.16 txty2Delay t0 tx0ttxL02ttx txL tx 2Delay t002ttxNot equal Time-varying 1.4.6 Linearity （线性）（线性）Additivity Scaling tytftytf2211 tytytftf2121 tytf taytaf tbytaytbftaf2121Chapter 1 Signals and SystemsExample 1.17 y ttx tExample 1.18 2y txtI
14、ts a linear system.Its a nonlinear system.Its a nonlinear system.Example 1.19 Rey nx n线性系统的特性线性系统的特性 f ty t 微分特性微分特性 df tdy tdtdt 积分特性积分特性 ttfdydChapter 1 Signals and Systems1.14 1.15 1.16 1.171.21 (d)(e)(f)1.22 (d)(g)1.23 1.24(a)(b)1.26(a)(b)1.27 1.31Homework:Chapter 1 Signals and SystemsChapter 1
15、Problems Solution112 tx-2 -1 0 1 2 t 1.21.A continuous-time signal x(t)is shown in Figure P1.21.Sketch and label carefully each of the following signals:(d)4/2(e)(f)3/23/2xtx txtu tx ttt 112 4 6 8 10 12 t 2/4tx112 tx-2 -1 0 1 2 t 112tx-2 -1 0 1 2 t 113 tutxtx0 1 2 t (f)3/23/2 3/23/23/23/2x tttxtxt -
16、3/2 0 3/2 t(-1/2)(-1/2)Chapter 1 Problems Solution10112 txt(b)1.23 Determine and sketch the even part of the signal.txe-2 -1 0 1 2 t1-2 -10 1 2 t2/12/1 txoChapter 1 Problems Solution1.27 A system may or may not be (1)Memoryless (2)Time invariant (3)Linear (4)Causal (5)Stable Determine which of these
17、 properties hold and which do not hold for each of the following continuous-time systems.a.22y tx txtLinear,Time-varying,with memory,not causal,stable b cos3y tt x tLinear,Time-varying,memoryless,causal,stable 2c ty txdLinear,Time-varying,with memory,not causal,not stableChapter 1 Problems Solution
18、0,t0d 2 t0y tx tx tLinear,Time-varying,with memory,Causal,Stable 0,0e 2 0 x ty tx tx tx tNonlinear,Time-invariant,with memory,Causal,Stable f /3y tx tLinear,Time-varying,with memory,not causal,Stable g dx tdty tLinear,Time-invariant,with memory,causal,not stableChapter 1 Problems Solution1.31 Consid
19、er an LTI system:tytx11 aDetermine and sketch?22tytx(b)Determine and sketch the response of the system(c)considered in part of(a)to the input x3(t).0121 tx1t20121 ty1t4310121 tx2t210121 tx3tChapter 1 Problems Solution 2111.2xtxtxt 2112ytytyt0 1 2 3 4 t21 ty22 3112.1xtxtxt 3111ytytyt20121 ty1t11ty201
20、21 ty3t1Chapter 1 Problems Solution例例 已知信号已知信号 及及 如图所示，试求：如图所示，试求：tfe 11tutf tf tf及及 的奇部的奇部1011 tfet101t2 11tutfChapter 1 Problems Solution1011t tx1Figure(a)01t tx2Figure(c)12014 ty1tFigure(b)1.Consider an LTI system whose response to the signal in2.Figure(a)is the signal illustrated in Figure(b).De
21、termine 3.and sketch carefully the response of the system to the input 4.depicted in Figure(c).tx1 ty1 tx2Chapter 1 Problems Solution2.Consider a continuous-time signal tx22 tx tx101121 txt(a)Sketch the signal .(b)Determine the even part(c)and odd part of 21sgn21x tt 212x nu nu nu n3.Sketch the following signals:4.(a)5.(b)Chapter 1 Problems Solution0 1 2 3 t21 tx0 1 n1-1 nx 0 1311 32 13 t,tx t t,t 0 t1-0 t0 0 t1 sgn t(a)b 112x nu nu nu nu n 1x nnnChapter 1 Problems Solution
