[工学]英文版《信号与系统》第9章讲义

1,Chapter 9 The Laplace Transform,2,9.1 The Laplace Transform,Defining,Laplace Transform,Dirichlet Condition 1 :,3,9.2 The Properties of ROC,Property 3: If is of finite duration and is absolutely integrable, then the ROC is the entire s-plane.,4,5,1.,2.,3.,Basic Laplace Transform-Pairs,6,Example 9.4,does not exist.,7,Example 9.8,left sided,two sided,right sided,8,9.3 The Inverse Laplace Transform,defining,9,Solution:,10,11,9.5 Properties of the Laplace Transform,9.5.1 Linearity of the Laplace Transform,12,9.5.2 Time Shifting,Example,Poles:,13,9.5.3 Shifting in s-Domain,14,When,15,16,9.5.4 Time Scaling,When,17,9.5.5 Conjugation,9.5.6 Convolution Property,18,9.5.7 Differentiation in the Time Domain,19,20,21,9.5.8 Differentiation in the s-Domain,22,more generally,23,Poles:,24,9.7 Analysis and Characterization of LTI Systems Using the Laplace Transform,System Function or Transfer Function,9.7.1 Causality,25,For a system with a rational system function,9.7.2 Stability (稳定性）,Stable system:,when,converges,26,Example 9.20,Causal , unstable system,noncausal , stable system,anticausal , unstable system（反因果）,27,如果 为有理函数,Stability of Causal System,Consider the following causal systems,Stable,unstable,28,9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations,ROC,A ratio of polynomials in s,29, causal, stable,30,Solution,Causal,is the eigenfunction of system.,31,The system is unstable.,32,Causal,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,33,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,34,1. 的傅立叶变换收敛。,2.,35,3. 为一因果稳定系统的单位冲激响应。,4. 至少有一个极点。,5. 为有限长度信号。,ROC不变,36,6.,在s=-2处有极点,7.,无法判断正确与否。,37,9.8 System Function Algebra and Block Diagram Representations （方框图）,Example 9.31Consider the causal LTI syst