电子科大课堂讲义课堂版信号9章临时ppt课件.ppt
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Chapter 9 The Laplace Transform Chapter 9 The Laplace Transform§9.1 The Laplace TransformDefining ——Laplace TransformDirichlet Condition 1 : Chapter 9 The Laplace TransformPoles:Zeros:1. The direction of signals2. The position of polesROC of X(s)§9.2 The Properties of ROC Chapter 9 The Laplace Transform1.2.3.Basic Laplace Transform-Pairs Chapter 9 The Laplace TransformExample 9.8left sidedtwo sidedright sided Chapter 9 The Laplace Transform§9.3 The Inverse Laplace TransformExample 9.9Determine the inverse Laplace transform for all possible ROC. Chapter 9 The Laplace Transform§9.5 Properties of the Laplace Transform§9.5.1 Linearity of the Laplace Transform Chapter 9 The Laplace Transform§9.5.2 Time ShiftingExample Poles:pole-zero plot Chapter 9 The Laplace Transform§9.5.3 Shifting in s-DomainROC的边境平移的边境平移 Chapter 9 The Laplace Transform§9.5.4 Time Scaling When Chapter 9 The Laplace Transform§9.5.5 Conjugation§9.5.6 Convolution Property Chapter 9 The Laplace Transform§9.5.7 Differentiation in the Time Domain Chapter 9 The Laplace TransformExample Determine §9.5.8 Differentiation in the s-Domain Chapter 9 The Laplace Transform Chapter 9 The Laplace TransformExampleDetermine Poles: Chapter 9 The Laplace Transform§9.7 Analysis and Characterization of LTI Systems Using the Laplace Transform——System Function or Transfer Function§9.7.1 CausalityCausal Chapter 9 The Laplace TransformFor a system with a rational system function,causal§9.7.2 Stability (稳定性〕定性〕Stable system:whenstableconverges Chapter 9 The Laplace TransformExample 9.20Causal , unstable systemnoncausal , stable systemanticausal , unstable system〔反因果〕〔反因果〕 系统因果、稳定系统因果、稳定 Chapter 9 The Laplace Transform的极点均在的极点均在 轴左侧，轴左侧，且且假设假设 为有理函数为有理函数Stability of Causal SystemConsider the following causal systems——Stable ——unstable Chapter 9 The Laplace Transform§9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations ROCA ratio of polynomials in s Chapter 9 The Laplace TransformExample 9.25Consider an LTI system with input ,Output , determine the system function.Example Consider a causal LTI system ,b——unknown constantDetermine the system function and b. Chapter 9 The Laplace TransformThe system is unstable. Chapter 9 The Laplace TransformExample 9.26 An LTI system: 1. The system is causal. 2. is rational and has only two poles: s= - 2 and s=4. 3. 4. Determine Example 9.26 An LTI system: 1. The system is causal. 2. is rational and has only two poles: s=-2 and s=-4. 3. 4. Determine Chapter 9 The Laplace TransformExample 9.27 知一因果稳定系统，知一因果稳定系统， 为有理函数，有一极点为有理函数，有一极点在在s=-2处，原点〔处，原点〔s=0〕处没有零点，其他零极点未知，〕处没有零点，其他零极点未知，判别以下说法能否正确。
判别以下说法能否正确1. 的傅立叶变换收敛的傅立叶变换收敛在在 收敛收敛2. 3. 为一因果稳定系统的单位冲激呼应为一因果稳定系统的单位冲激呼应4. 至少有一个极点至少有一个极点5. 为有限长度信号为有限长度信号 Chapter 9 The Laplace TransformROC不不变 Chapter 9 The Laplace Transform6. 在在s=-2处有极点有极点在在s=+2处有极点处有极点7.无法判无法判别正确与否正确与否 §9.8 LTI 系系统的方框的方框图〔信号流〔信号流图〕表示〕表示k——前向通路的序号前向通路的序号gk——第第k条前向通路的增益条前向通路的增益△△k——去掉第去掉第k条前向通路后条前向通路后,余下的子流余下的子流图的特征行列式的特征行列式△△——信号流信号流图的特征行列式的特征行列式 Chapter 9 The Laplace Transform一一 Mason 增益公式增益公式 Example 9.31 Chapter 9 The Laplace Transform Chapter 9 The Laplace Transform二二 系统的方框图〔信号流图〕模拟系统的方框图〔信号流图〕模拟两个根本商定：两个根本商定：1. 假定一切的假定一切的环路均相互接触；路均相互接触；2. 假定每一前向通路与一切的假定每一前向通路与一切的环路相互接触；路相互接触； Chapter 9 The Laplace TransformExample Consider the causal LTI system1. 直接模直接模拟2. 级联型模型模拟3. 并并联型模型模拟 Chapter 9 The Laplace TransformHomework: 9.2 9.5 9.7 9.8 9.9 9.13 9.21(a,b,i,j) 9.22(a,b,c,d) 9.28 9.31 9.32 9.33 9.35 9.45 ExampleDetermine Chapter 9 The Laplace Transform 。
