信号与系统双语奥本海姆第二章

1,Chapter 2,Linear Time-invariant Systems,2,Example 1 an LTI system,3,2.1 Discrete-time LTI Systems : The Convolution Sum（卷积和）,2.1.1 The Representation of Discrete-Time Signalsin Terms of impulses,4,2.1.2 The Discrete-Time Unit Impulse Responses and the Convolution-Sum Representation of LTI Systems,The Unit Impulse Responses单位冲激响应,2. Convolution-Sum （卷积和）,系统在n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n时刻的响应,5,3. 卷积和的计算, 利用定义计算,例2.3, 图解法,6,7,8, 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, 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,9,2.2 Continuous-Time LTI Systems : The Convolution Integral （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 Systems,10,2.3 卷积的计算,1. 由定义计算卷积积分,2. 图解法,例2.7 求下列两信号的卷积,3. 利用卷积积分的运算性质求解,11,2.3 Properties of LTI Systems,LTI系统的特性可由单位冲激响应完全描述,Example 2.9, LTI system, Nonlinear System, Time-variant System,12,2.3.1 Properties of Convolution Integral and Convolution Sum,1. The Commutative Property (交换律）,13,2. The Distributive Property (分配律）,14,3. The Associative Property (结合律）,15,4. 含有冲激的卷积,16,5. 卷积的微分、积分性质, 微分性质, 积分性质, 推广形式,n0 微分n0 积分,17,特殊地 n=1 m=-1,18,Example Consider the convolution of the two signals,19,6 几种典型系统, 恒等系统, 微分器, 积分器, 延迟器, 累加器,20,2.3.4 LTI Systems with and without Memory,1. Discrete-time System,An LTI system without memory,2. Continuous-time System,An LTI system without memory,21,2.3.5 Invertibility of LTI SystemsLTI系统的可逆性,22,2.3.6 Causality for LTI SystemsLTI系统的因果性,1. Discrete-time System,2. Continuous-time System,23,Consider a LTI system,For any time t0,The system is initial rest. (初始松弛）,24,2.3.7 Stability for LTI Systems (稳定性）,1. Discrete-time System,Absolutely summable （绝对可加）,2. Continuous-time System,Absolutely integrable （绝对可积 ）,25,26,27,2.3.8 The Unit Step Response of an LTI SystemsLTI系统的单位阶跃响应,Discrete-time System,Continuous-time System,Unit Step Response,Unit Step Response,28,2.4 Singularity Functions (奇异函数）,2.4.1 The Unit Impulse as an Idealized Short Pulse,29,Example 2.16,30,Example 2.17,31,2.4.2 Defining the Unit Impulse through Convolution单位冲激的卷积定义,For any x(t),For any normal ,which is continuous at time t=0.,32,2.4.3 Unit Doublets and Other Singularity Functions单位冲激偶和其它奇异函数,1.,In general ,33,3. Properties of Unit Doublets （冲激偶的性质）,Derivatives of different orders of the unit impulse单位冲激的各阶积分,34,2. 5 Causal LTI Systems described by Differential and Difference Equations,2. 5.1 Linear Constant-coefficient Differential Equations,一 经典解法,Homogeneous solution,Natural Response,Particular Solution,Forced Response,35,不是特征单根 是特征单根,或,36,37,由初始状态唯一决定,由零初始状态及输入共同决定,由初始状态及输入决定,函数形式由输入信号决定,零输入零状态解法,经典解法,三 两种响应分解形式的关系,二 零输入、零状态解法,38,Zero-input response,Zero-state response,3. Full response,39,40,41,2.5.2 Linear Constant-coefficient Difference Equations 线性常系数差分方程,Nth order,Recursive Solution（递推算法）,42,2. Typical solution,Homogeneous solution,Natural Response,Particular Solution,Forced Response,43, Particular solution (Forced Response),不是特征单根 是特征单根,或,44,3. 零输入、零状态解法,Zero-inputResponse,4. 两种响应分解形式的关系,Zero-stateResponse,45,Solution 1,Homogeneous Solution,Particular Solution,Full Solution,46,2. 5.3 Block Diagram Representations of First-Order System 一阶系统的方框图表示,1. Discrete-time systems,Addition,Multiplication by a coefficient,Delay,Recursive Equation,47,2. Continuous-time systems,Addition,Multip