信号与系统双语奥本海姆

1、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 Systems2.1 Discrete-time LTI Systems : The Convolution Sum卷积和2.1.1 The Representation of Discrete-Time Signalsin Terms of impulsesExample 2n3 Chapter 2 LTI Systems2.1

2、.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4 Chapter 2 LTI Systems3. 卷积和的计算 利用定义计算例2.3 图解法Example 2.4Determine the output signal 5图解法步骤：反折 平移 求乘积 对每一个n求和循环6

3、 Chapter 2 LTI SystemsExample 2.4Determine the output signal 7 Chapter 2 LTI Systems 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Example 3Determine 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8 Chapter 2 LTI Systems2.2 Continuous-Time LTI Systems : The Convolution Integral 卷积积分2.2.1 The Representation of Continuous-Time Signalsin

4、 Terms of impulsesSifting Property2.2.2 The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems9 Chapter 2 LTI Systems2.3 卷积的计算1. 由定义计算卷积积分例2.62. 图解法例2.7 求以下两信号的卷积其余t其余t3. 利用卷积积分的运算性质求解10 Chapter 2 LTI Systems2.3 Properties of LTI SystemsLTI系统的特性可由单位冲激响应完

5、全描述Example 2.9 LTI system Nonlinear System Time-variant System11 Chapter 2 LTI Systems2.3.1 Properties of Convolution Integral and Convolution Sum 1. The Commutative Property (交换律12 Chapter 2 LTI Systems2. The Distributive Property (分配律13 Chapter 2 LTI Systems3. The Associative Property (结合律Commutat

6、ive PropertyAssociative Property14 Chapter 2 LTI Systems4. 含有冲激的卷积15 Chapter 2 LTI Systems5. 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16 Chapter 2 LTI Systems特殊地 n=1 m=-1Example otherwiseotherwise Consider the convolution of the two signals17Example Consider the convolution of the two signals Chapter 2 LT

7、I Systems18 Chapter 2 LTI Systems6 几种典型系统 恒等系统 微分器 积分器 延迟器 累加器19 Chapter 2 LTI Systems2.3.4 LTI Systems with and without Memory 1. Discrete-time SystemAn LTI system without memory2. Continuous-time SystemAn LTI system without memory20 Chapter 2 LTI Systems2.3.5 Invertibility of LTI SystemsLTI系统的可逆性S

8、ystem Inverse System identity system (恒等系统）21 Chapter 2 LTI Systems2.3.6 Causality for LTI SystemsLTI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）For any time t0The system is initial rest. (初

9、始松弛23 Chapter 2 LTI Systems2.3.7 Stability for LTI Systems (稳定性1. Discrete-time System Stable SystemAbsolutely summable （绝对可加）2. Continuous-time System Stable SystemAbsolutely integrable （绝对可积 ）24卷积的微分、积分性质 Chapter 2 LTI SystemsProperties of LTI systemsAn LTI system without memoryAn LTI system witho

10、ut memoryInvertibility of LTI Systems25 Chapter 2 LTI SystemsDiscrete-time SystemContinuous-time System Causal system Causal system Stable System Stable System26 Chapter 2 LTI Systems2.3.8 The Unit Step Response of an LTI SystemsLTI系统的单位阶跃响应Discrete-time SystemContinuous-time SystemUnit Step Respons

11、eUnit Step Response27 Chapter 2 LTI Systems2.4 Singularity Functions (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 2.1730Define Chapter 2 LTI Systems2.4.2 Defining the Unit Impulse through Convolu

12、tion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 Systems2.4.3 Unit Doublets and Other Singularity Functions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Derivatives of different orders of the unit impulse单位

13、冲激的各阶积分33 Chapter 2 LTI Systems2. 5 Causal LTI Systems described by Differential and Difference Equations 2. 5.1 Linear Constant-coefficient Differential Equations一 经典解法Homogeneous solutionNatural ResponseParticular SolutionForced Response34 Chapter 2 LTI Systems输入 特解 C （常数）B （常数） 不是特征单根 是特征单根或35 Ch

14、apter 2 LTI SystemsExample 2.14(a) The system is initial restDetermine the output36 Chapter 2 LTI Systems由初始状态唯一决定零输入响应由零初始状态及输入共同决定零状态响应由初始状态及输入决定自然响应函数形式由输入信号决定受迫响应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37 Chapter 2 LTI SystemsZero-input responseZero-state response3. Full responseExample 2.14Determin

15、e the output38 Chapter 2 LTI SystemsDefining the Unit Impulse through Convolution39Homogeneous Solution Natural Response Particular SolutionForced Response 40 Chapter 2 LTI Systems2.5.2 Linear Constant-coefficient Difference Equations 线性常系数差分方程Nth orderRecursive Solution递推算法Example 2.15(a) The syste

16、m is initial rest, and the input Determine the output41 Chapter 2 LTI Systems2. Typical solutionHomogeneous solutionNatural ResponseParticular SolutionForced Response42 Chapter 2 LTI Systems Particular solution (Forced Response)输入 特解 不是特征单根 是特征单根或43 Chapter 2 LTI Systems3. 零输入、零状态解法Zero-inputRespons

17、e 4. 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 Systems2. 5.3 Block Diagram Representations of First-Order System 一阶系统的方框图表示1. Discrete-time systemsThre

18、e 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 SystemsInitial Condition48 Chapter 2 LTI Systems作业： 2.20 2.23 2.40 2.46 2.4749 Chapter 2 LTI Systems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：反折 平移 求乘积 对每一个n求和循环51 Chapter 2 LTI Systems52卷积的微分、积分性质 Chapter 2 LTI SystemsProperties of LTI systemsAn LTI system without memoryAn LTI system without memo