英文版《信号与系统》讲义

1、 Chapter 9 The Laplace Transform1 Chapter 9 The Laplace Transform9.1 The Laplace TransformDefining Laplace TransformDirichlet Condition 1 :2 Chapter 9 The Laplace TransformPoles:Zeros:1. The direction of signals2. The position of polesROC of X(s)9.2 The Properties of ROCProperty 3: If is of finite d

2、uration and is absolutely integrable, then the ROC is the entire s-plane.3 Chapter 9 The Laplace TransformProperty 7: If the Laplace transform of is rational, is right sided, is left sided,Property 6: If is two sided, 4 Chapter 9 The Laplace Transform1.2.3.Basic Laplace Transform-Pairs5 Chapter 9 Th

3、e Laplace TransformExample 9.4does not exist.pole-zero plot6 Chapter 9 The Laplace TransformExample 9.8left sidedtwo sidedright sided7 Chapter 9 The Laplace Transform9.3 The Inverse Laplace Transformdefining8 Chapter 9 The Laplace TransformExample 9.9Determine the inverse Laplace transform for all p

4、ossible ROC.Solution:9 Chapter 9 The Laplace Transform10 Chapter 9 The Laplace Transform9.5 Properties of the Laplace Transform9.5.1 Linearity of the Laplace Transform11 Chapter 9 The Laplace Transform9.5.2 Time ShiftingExample Poles:pole-zero plot12 Chapter 9 The Laplace Transform9.5.3 Shifting in

5、s-DomainROC的边界平移13 Chapter 9 The Laplace TransformWhen 14 Chapter 9 The Laplace Transform15 Chapter 9 The Laplace Transform9.5.4 Time Scaling When 16 Chapter 9 The Laplace Transform9.5.5 Conjugation9.5.6 Convolution Property17 Chapter 9 The Laplace Transform9.5.7 Differentiation in the Time Domain18

6、 Chapter 9 The Laplace TransformExample Determine 19 Chapter 9 The Laplace Transform209.5.8 Differentiation in the s-Domain Chapter 9 The Laplace Transform21 Chapter 9 The Laplace Transformmore generally, 22 Chapter 9 The Laplace TransformExampleDetermine Poles:23 Chapter 9 The Laplace Transform9.7

7、Analysis and Characterization of LTI Systems Using the Laplace TransformSystem Function or Transfer Function9.7.1 CausalityCausal 24 Chapter 9 The Laplace TransformFor a system with a rational system function,causal9.7.2 Stability (稳定性Stable system:whenstableconverges25 Chapter 9 The Laplace Transfo

8、rmExample 9.20Causal , unstable systemnoncausal , stable systemanticausal , unstable system反因果26系统因果、稳定 Chapter 9 The Laplace Transform的极点均在 轴左侧，且如果 为有理函数Stability of Causal SystemConsider the following causal systemsStable unstable 27 Chapter 9 The Laplace Transform9.7.3 LTI Systems Characterized b

9、y Linear Constant-Coefficient Differential Equations ROCA ratio of polynomials in s 28 Chapter 9 The Laplace TransformExample 9.25Consider an LTI system with input ,Output , determine the system function. causal stable29 Chapter 9 The Laplace TransformExample Consider a causal LTI system ,bunknown c

10、onstantDetermine the system function and b.Solution Causal is the eigenfunction of system.30 Chapter 9 The Laplace TransformThe system is unstable.31 Chapter 9 The Laplace TransformCausal 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

11、. Determine 32 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 33 Chapter 9 The Laplace TransformExample 9.27 已知一因果稳定系统， 为有理函数，有一极点在s=-2处，原点（s=0）处没有零点，其余零极点未知，判断下列说法是否正确。1. 的傅立叶变换收敛。在 收敛2.343. 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。 Chapter 9 The Laplace TransformROC不变35 Chapter 9 The Laplace Transform6. 在s=-2处有极点在s=+2处有极点7.无法判断正确与否。36 Chapter 9 The Laplace Transform9.8 System Function Algebra and Block Diagram Repr