信號(hào)與系統(tǒng)雙語奧本海姆

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卷積和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單位沖激響應(yīng)2. Convolution-Sum 卷積和系統(tǒng)在n時(shí)刻的輸出包含所有時(shí)刻輸入脈沖的影響k時(shí)刻的脈沖在n時(shí)刻的響應(yīng)4 Chapter 2 LTI Systems3. 卷積和的計(jì)算 利用定義計(jì)算例2.3 圖解法Example 2.4Determine the output signal 5圖解法步驟：反折 平移 求乘積 對(duì)每一個(gè)n求和循環(huán)6

3、 Chapter 2 LTI SystemsExample 2.4Determine the output signal 7 Chapter 2 LTI Systems 不帶進(jìn)位的普通乘法適用于因果序列或有限長度序列之間的卷積Example 3Determine 多項(xiàng)式算法適用于有限長度序列利用多項(xiàng)式算法求卷積和的逆運(yùn)算8 Chapter 2 LTI Systems2.2 Continuous-Time LTI Systems : The Convolution Integral 卷積積分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 卷積的計(jì)算1. 由定義計(jì)算卷積積分例2.62. 圖解法例2.7 求以下兩信號(hào)的卷積其余t其余t3. 利用卷積積分的運(yùn)算性質(zhì)求解10 Chapter 2 LTI Systems2.3 Properties of LTI SystemsLTI系統(tǒng)的特性可由單位沖激響應(yīng)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 (交換律12 Chapter 2 LTI Systems2. The Distributive Property (分配律13 Chapter 2 LTI Systems3. The Associative Property (結(jié)合律Commutat

6、ive PropertyAssociative Property14 Chapter 2 LTI Systems4. 含有沖激的卷積15 Chapter 2 LTI Systems5. 卷積的微分、積分性質(zhì) 微分性質(zhì) 積分性質(zhì) 推廣形式n0 微分n0 積分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 幾種典型系統(tǒng) 恒等系統(tǒng) 微分器 積分器 延遲器 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系統(tǒng)的可逆性S

8、ystem Inverse System identity system (恒等系統(tǒng)）21 Chapter 2 LTI Systems2.3.6 Causality for LTI SystemsLTI系統(tǒng)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 (穩(wěn)定性1. Discrete-time System Stable SystemAbsolutely summable （絕對(duì)可加）2. Continuous-time System Stable SystemAbsolutely integrable （絕對(duì)可積 ）24卷積的微分、積分性質(zhì) 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系統(tǒng)的單位階躍響應(yīng)Discrete-time SystemContinuous-time SystemUnit Step Respons

11、eUnit Step Response27 Chapter 2 LTI Systems2.4 Singularity Functions (奇異函數(shù)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單位沖激的卷積定義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單位沖激偶和其它奇異函數(shù) 1. In general ,2.For any 32 Chapter 2 LTI Systems3. Properties of Unit Doublets 沖激偶的性質(zhì)Derivatives of different orders of the unit impulse單位

13、沖激的各階積分33 Chapter 2 LTI Systems2. 5 Causal LTI Systems described by Differential and Difference Equations 2. 5.1 Linear Constant-coefficient Differential Equations一 經(jīng)典解法Homogeneous solutionNatural ResponseParticular SolutionForced Response34 Chapter 2 LTI Systems輸入 特解 C （常數(shù)）B （常數(shù)） 不是特征單根 是特征單根或35 Ch

14、apter 2 LTI SystemsExample 2.14(a) The system is initial restDetermine the output36 Chapter 2 LTI Systems由初始狀態(tài)唯一決定零輸入響應(yīng)由零初始狀態(tài)及輸入共同決定零狀態(tài)響應(yīng)由初始狀態(tài)及輸入決定自然響應(yīng)函數(shù)形式由輸入信號(hào)決定受迫響應(yīng)零輸入零狀態(tài)解法經(jīng)典解法三 兩種響應(yīng)分解形式的關(guān)系二 零輸入、零狀態(tài)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 線性常系數(shù)差分方程N(yùn)th orderRecursive Solution遞推算法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)輸入 特解 不是特征單根 是特征單根或43 Chapter 2 LTI Systems3. 零輸入、零狀態(tài)解法Zero-inputRespons

17、e 4. 兩種響應(yīng)分解形式的關(guān)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 一階系統(tǒng)的方框圖表示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作業(yè)： 2.20 2.23 2.40 2.46 2.4749 Chapter 2 LTI Systems作業(yè)：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圖解法步驟：反折 平移 求乘積 對(duì)每一個(gè)n求和循環(huán)51 Chapter 2 LTI Systems52卷積的微分、積分性質(zhì) Chapter 2 LTI SystemsProperties of LTI systemsAn LTI system without memoryAn LTI system without memo