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1、电子科大讲义课堂信号ch1 Still waters run deep.流静水深流静水深,人静心深人静心深 Where there is life,there is hope。有生命必有希望。有生命必有希望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:20072Chapter 1 Signals and Systems
2、1.1 Basic Discrete-Time Signals 1.1.1 The Discrete-Time Unit Impulse and Unit Step SequencesUnit Impulse 1n=020 n 0Unit Step1n 020 n 00 t 00 t10 t 02.Unit Impulse Function 0 t(1)5 0 积分区间积分区间 0 积分区间积分区间Chapter 1 Signals and Systems 1.2.2 The Properties of Unit Impulse Functions1.Sampling and Sifting
3、propertiesIf f(t)is continuous at the point of t=0Sampling property Sifting property6In General2.Scaling property3.If a is real,a 0Specially a=-1 Even functionChapter 1 Signals and Systems74.Properties of Unit Doublets（冲激偶的性质）（冲激偶的性质）3.DefiningFor any Chapter 1 Signals and Systems8 1.2.3 Continuous-
4、Time Complex Exponential and Sinusoidal SignalsChapter 1 Signals and Systems General Complex Exponential Signals 91.3 Transformations of the independent variable1.Time shift2.Time reversal3.Time-scaling4.Even and Odd Signals5.Differential and Integral Chapter 1 Signals and Systems10Example 1.1 Given
5、 the signal x(t)x(-3/2 t+1)0 1 2 t1Solution 1-1 0 1 t1Time-shift-1 0 1 t1Time-reversal-2/3 0 2/3 t1Time-scalingSolution 2-2 -1 0 t1Time-reversal-4/3 -2/3 0 t1Time-scaling-2/3 0 2/3 t1Time-shiftChapter 1 Signals and Systems11信号的基本表示信号的基本表示-0 t-0 t 0 t0 1 t 110 1 t 0 t1-1 0 1 t1-1 0 t10 1 t 20 1 2 t 1
6、Chapter 1 Signals and Systems12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 1.40(a),determinethe derivative of x(t).2 1 0 1 2 3 4 t-1x(t)0 1 2 3 4 t(2)(-3)(2)Chapter 1 Signals and Systems13Continuous-Time System Discrete-Time System N-order Linear Constant-coefficientDifferential Equati
7、on N-order Linear Constant-coefficientDifference Equation 1.4 Continuous-time and discrete-time systemsChapter 1 Signals and Systems14 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 summer d
8、elay integrateSystems with memoryChapter 1 Signals and Systems15 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）。SystemInverse System noninvertible systems不可逆系统不可逆系统Chapter 1 Signals and Systems16 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
9、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 Causal systemsChapter 1 Signals and Systems17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.Not Causal 1.4.4 Stability （稳定性）（稳定性）Stable System not stable stableChapter 1 Signals and Systems18 1.4.5 Time Invariance （时不变性）（时
10、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.If Time invariant时不变时不变 Consider a continuous-time system Delay t0LLDelay t0=time invariantsystem time-varyingsystemChapter 1 Signals and Systems19Example 1.14Delay t0LLDelay t0Equal Time invariantE
11、xample 1.15Not equal Time-varyingDelay n0LLDelay n0Chapter 1 Signals and Systems20Example 1.16Delay t0LLDelay t0Not equal Time-varying 1.4.6 Linearity （线性）（线性）Additivity Scaling Chapter 1 Signals and Systems21Example 1.17Example 1.18Its a linear system.Its a nonlinear system.Its a nonlinear system.E
12、xample 1.19线性系统的特性线性系统的特性 微分特性微分特性 积分特性积分特性Chapter 1 Signals and Systems221.14 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 Systems23Chapter 1 Problems Solution-2 -1 0 1 2 t 1.21.A continuous-time signal x(t)is shown in Figure P1.21.Sketch a
13、nd label carefully each of the following signals:4 6 8 10 12 t 24-2 -1 0 1 2 t-2 -1 0 1 2 t 0 1 2 t-3/2 0 3/2 t(-1/2)(-1/2)Chapter 1 Problems Solution25(b)1.23 Determine and sketch the even part of the signal.-2 -1 0 1 2 t-2 -10 1 2 tChapter 1 Problems Solution261.27 A system may or may not be (1)Me
14、moryless (2)Time invariant (3)Linear (4)Causal (5)Stable Determine which of these properties hold and which do not hold for each of the following continuous-time systems.Linear,Time-varying,with memory,not causal,stableLinear,Time-varying,memoryless,causal,stableLinear,Time-varying,with memory,not c
15、ausal,not stableChapter 1 Problems Solution27Linear,Time-varying,with memory,Causal,StableNonlinear,Time-invariant,with memory,Causal,StableLinear,Time-varying,with memory,not causal,StableLinear,Time-invariant,with memory,causal,not stableChapter 1 Problems Solution281.31 Consider an LTI system:Det
16、ermine and sketch(b)Determine and sketch the response of the system(c)considered in part of(a)to the input x3(t).Chapter 1 Problems Solution290 1 2 3 4 tChapter 1 Problems Solution30例例 已知信号已知信号 及及 如图所示，试求：如图所示，试求：及及 的奇部的奇部Chapter 1 Problems Solution31Figure(a)Figure(c)Figure(b)1.Consider an LTI syst
17、em whose response to the signal in2.Figure(a)is the signal illustrated in Figure(b).Determine 3.and sketch carefully the response of the system to the input 4.depicted in Figure(c).Chapter 1 Problems Solution322.Consider a continuous-time signal(a)Sketch the signal .(b)Determine the even part(c)and odd part of 3.Sketch the following signals:4.(a)5.(b)Chapter 1 Problems Solution330 1 2 3 t210 1 n1-1(a)Chapter 1 Problems Solution34