信號與系統(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2. Convolution-Sum 卷積和系統(tǒng)在n時刻的輸出包含所有時刻輸入脈沖的影響k時刻的脈沖在n時刻的響應4 Chapter 2 LTI Systems3. 卷積和的計算 利用定義計算例2.3 圖解法Example 2.4Determine the output signal 5圖解法步驟：反折 平移 求乘積 對每一個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 多項式算法適用于有限長度序列利用多項式算法求卷積和的逆運算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 卷積的計算1. 由定義計算卷積積分例2.62. 圖解法例2.7 求以下兩信號的卷積其余t其余t3. 利用卷積積分的運算性質求解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 微分性質 積分性質 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 （絕對可加）2. Continuous-time System Stable SystemAbsolutely integrable （絕對可積 ）24卷積的微分、積分性質 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Discrete-time SystemContinuous-time SystemUnit Step Respons

11、eUnit Step Response27 Chapter 2 LTI Systems2.4 Singularity Functions (奇異函數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 1. In general ,2.For any 32 Chapter 2 LTI Systems3. Properties of Unit Doublets 沖激偶的性質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 經典解法Homogeneous solutionNatural ResponseParticular SolutionForced Response34 Chapter 2 LTI Systems輸入 特解 C （常數）B （常數） 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由零初始狀態(tài)及輸入共同決定零狀態(tài)響應由初始狀態(tài)及輸入決定自然響應函數形式由輸入信號決定受迫響應零輸入零狀態(tài)解法經典解法三 兩種響應分解形式的關系二 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 線性常系數差分方程Nth 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. 兩種響應分解形式的關系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 對每一個n求和循環(huán)51 Chapter 2 LTI Systems52卷積的微分、積分性質 Chapter 2 LTI SystemsProperties of LTI systemsAn LTI system without memoryAn LTI system without memo