信号与系统双语奥本海姆.ppt

Chapter 2Linear Time-invariant Systems1 Chapter 2 LTI SystemsExample 1 an LTI system0 2 t10 1 2 t1L0 2 4 t1-10 2 4 t1L2 Chapter 2 LTI Systems§2.1 Discrete-time LTI Systems : The Convolution Sum〔卷积和〕〔卷积和〕§2.1.1 The Representation of Discrete-Time Signalsin Terms of impulsesExample 2n3 Chapter 2 LTI Systems§2.1.2 The Discrete-Time Unit Impulse Responses and the Convolution-Sum Representation of LTI Systems 1.The Unit Impulse Responses单位冲激响应单位冲激响应2. Convolution-Sum 〔卷积和〕〔卷积和〕系统在系统在n时刻的输出包含所有时刻输入脉冲的影响时刻的输出包含所有时刻输入脉冲的影响k时刻的脉冲在时刻的脉冲在n时刻的响应时刻的响应4 Chapter 2 LTI Systems3. 卷积和的计算卷积和的计算①① 利用定义计算利用定义计算例例2.3②② 图解法图解法Example 2.4Determine the output signal 5图解法步骤：图解法步骤：㈠㈠反折反折㈡㈡ 平移平移㈢㈢ 求乘积求乘积㈣㈣ 对每一个对每一个n求和求和循循环环6 Chapter 2 LTI SystemsExample 2.4Determine the output signal 7 Chapter 2 LTI Systems③③ 不带进位的普通乘法不带进位的普通乘法——适用于因果序列或有限长度序列之间的卷积适用于因果序列或有限长度序列之间的卷积Example 3Determine ④④ 多项式算法〔适用于有限长度序列〕多项式算法〔适用于有限长度序列〕利用多项式算法求卷积和的逆运算利用多项式算法求卷积和的逆运算8 Chapter 2 LTI Systems§2.2 Continuous-Time LTI Systems : The Convolution Integral 〔卷积积分〕〔卷积积分〕§2.2.1 The Representation of Continuous-Time Signalsin Terms of impulses——Sifting Property§2.2.2 The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems9 Chapter 2 LTI Systems§2.3 卷积的计算卷积的计算1. 由定义计算卷积积分由定义计算卷积积分例例2.62. 图解法图解法例例2.7 求以下两信号的卷积求以下两信号的卷积其余其余t其余其余t3. 利用卷积积分的运算性质求解利用卷积积分的运算性质求解10 Chapter 2 LTI Systems§2.3 Properties of LTI SystemsLTI系统的特性可由单位冲激响应完全描述系统的特性可由单位冲激响应完全描述Example 2.9①① LTI system②② Nonlinear System③③ Time-variant System11 Chapter 2 LTI Systems§2.3.1 Properties of Convolution Integral and Convolution Sum 1. The Commutative Property (交换律〕交换律〕12 Chapter 2 LTI Systems2. The Distributive Property (分配律〕分配律〕13 Chapter 2 LTI Systems3. The Associative Property (结合律〕结合律〕Commutative PropertyAssociative Property14 Chapter 2 LTI Systems4. 含有冲激的卷积含有冲激的卷积①①②②15 Chapter 2 LTI Systems5. 卷积的微分、积分性质卷积的微分、积分性质①① 微分性质微分性质②② 积分性质积分性质③③ 推广形式推广形式n>0 微分微分n<0 积分积分16 Chapter 2 LTI Systems特殊地特殊地 n=1 m=-1Example otherwiseotherwise Consider the convolution of the two signals17Example Consider the convolution of the two signals Chapter 2 LTI Systems18 Chapter 2 LTI Systems6 几种典型系统几种典型系统①① 恒等系统恒等系统②② 微分器微分器③③ 积分器积分器④④ 延迟器延迟器⑤⑤ 累加器累加器19 Chapter 2 LTI Systems§2.3.4 LTI Systems with and without Memory 1. Discrete-time SystemAn LTI system without memory2. Continuous-time SystemAn LTI system without memory20 Chapter 2 LTI Systems§2.3.5 Invertibility of LTI SystemsLTI系统的可逆性系统的可逆性System Inverse System identity system (恒等系统）恒等系统）21 Chapter 2 LTI Systems§2.3.6 Causality for LTI SystemsLTI系统的因果性系统的因果性1. Discrete-time System Causal system2. Continuous-time System Causal system22 Chapter 2 LTI SystemsConsider a LTI system Causal Initial Rest (初始松弛）初始松弛）For any time t0The system is initial rest. (初始松弛〕初始松弛〕23 Chapter 2 LTI Systems§2.3.7 Stability for LTI Systems (稳定性〕稳定性〕1. Discrete-time System Stable SystemAbsolutely summable （绝对可加）（绝对可加）2. Continuous-time System Stable SystemAbsolutely integrable （绝对可积（绝对可积 ））24卷积的微分、积分性质卷积的微分、积分性质 Chapter 2 LTI SystemsProperties of LTI systemsAn LTI system without memoryAn LTI system without memoryInvertibility of LTI Systems25 Chapter 2 LTI SystemsDiscrete-time SystemContinuous-time System Causal system Causal system Stable System Stable System26 Chapter 2 LTI Systems§2.3.8 The Unit Step Response of an LTI SystemsLTI系统的单位阶跃响应系统的单位阶跃响应Discrete-time SystemContinuous-time SystemUnit Step ResponseUnit Step Response27 Chapter 2 LTI Systems§2.4 Singularity Functions (奇异函数〕奇异函数〕§2.4.1 The Unit Impulse as an Idealized Short Pulse0 △△ tExample 2.16Example 2.1728 Chapter 2 LTI SystemsExample 2.1629 Chapter 2 LTI SystemsExample 2.1730Define Chapter 2 LTI Systems§2.4.2 Defining the Unit Impulse through Convolution单位冲激的卷积定义单位冲激的卷积定义For any x(t)For any normal ,which is continuous at time t=0.31 Chapter 2 LTI Systems§2.4.3 Unit Doublets and Other Singularity Functions单位冲激偶和其它奇异函数单位冲激偶和其它奇异函数 1. In general ,2.For any 32 Chapter 2 LTI Systems3. Properties of Unit Doublets 〔冲激偶的性质〕〔冲激偶的性质〕①①②②③③4.Derivatives of different orders of the unit impulse单位冲激的各阶积分单位冲激的各阶积分33 Chapter 2 LTI Systems§2. 5 Causal LTI Systems described by Differential and Difference Equations §2. 5.1 Linear Constant-coefficient Differential Equations一一 经典解法经典解法Homogeneous solutionNatural ResponseParticular SolutionForced Response34 Chapter 2 LTI Systems输输入入 特解特解 C （常数）（常数）B （常数）（常数） α不是特征单根不是特征单根α 是特征单根是特征单根或或35 Chapter 2 LTI SystemsExample 2.14(a) The system is initial restDetermine the output36 Chapter 2 LTI Systems由初始状态由初始状态唯一决定唯一决定零输入响应零输入响应由零初始状态由零初始状态及输入共同决定及输入共同决定零状态响应零状态响应由初始状态由初始状态及输入决定及输入决定自然响应自然响应函数形式由函数形式由输入信号决定输入信号决定受迫响应受迫响应零输入零零输入零状态解法状态解法经典解法经典解法三三 两种响应分解形式的关系两种响应分解形式的关系二二 零输入、零状态解法零输入、零状态解法37 Chapter 2 LTI Systems1.Zero-input response2.Zero-state response3. Full responseExample 2.14Determine the output38 Chapter 2 LTI SystemsDefining the Unit Impulse through Convolution39Homogeneous Solution Natural Response Particular SolutionForced Response 40 Chapter 2 LTI Systems§2.5.2 Linear Constant-coefficient Difference Equations 线性常系数差分方程线性常系数差分方程Nth order1.Recursive Solution〔递推算法〕〔递推算法〕Example 2.15(a) The system is initial rest, and the input Determine the output41 Chapter 2 LTI Systems2. Typical solutionHomogeneous solutionNatural ResponseParticular SolutionForced Response42 Chapter 2 LTI Systems②② Particular solution (Forced Response)输输入入 特解特解 α不是特征单根不是特征单根α 是特征单根是特征单根或或43 Chapter 2 LTI Systems3. 零输入、零状态解法零输入、零状态解法Zero-inputResponse 4. 两种响应分解形式的关系两种响应分解形式的关系Zero-stateResponse 44 Chapter 2 LTI SystemsExample Consider an LTI system:Determine the full responseSolution 1Homogeneous SolutionParticular SolutionFull Solution45 Chapter 2 LTI Systems§2. 5.3 Block Diagram Representations of First-Order System 一阶系统的方框图表示一阶系统的方框图表示1. Discrete-time systemsThree basic operationsAddition Multiplication by a coefficientDelay DRecursive EquationDInitial rest :46 Chapter 2 LTI Systems2. Continuous-time systemsThree basic operationsAddition Multiplication by a coefficientIntegrator ∫47 Chapter 2 LTI Systems∫Initial Condition48 Chapter 2 LTI Systems作业：作业： 2.20 2.23 2.40 2.46 2.4749 Chapter 2 LTI Systems作业：作业：2.1 2.5 2.72.10 2.11 2.12 2.22 (a) (c)2.20 2.23 2.40 2.46 2.4750图解法步骤：图解法步骤：㈠㈠反折反折㈡㈡ 平移平移㈢㈢ 求乘积求乘积㈣㈣ 对每一个对每一个n求和求和循循环环51 Chapter 2 LTI Systems52卷积的微分、积分性质卷积的微分、积分性质 Chapter 2 LTI SystemsProperties of LTI systemsAn LTI system without memoryAn LTI system without memoryInvertibility of LTI Systems53 Chapter 2 LTI SystemsDiscrete-time SystemContinuous-time System Causal system Causal system Stable System Stable System54 Chapter 2 LTI SystemsDefining the Unit Impulse through Convolution55Homogeneous Solution Natural Response Particular SolutionForced Response 56。