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1、电子科大课堂讲义课堂版信号9章临时 Still waters run deep.流静水深流静水深,人静心深人静心深 Where there is life,there is hope。有生命必有希望。有生命必有希望 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
2、 polesROC of X(s)9.2 The Properties of ROC3 Chapter 9 The Laplace Transform1.2.3.Basic Laplace Transform-Pairs4 Chapter 9 The Laplace TransformExample 9.8left sidedtwo sidedright sided5 Chapter 9 The Laplace Transform9.3 The Inverse Laplace TransformExample 9.9Determine the inverse Laplace transform
3、 for all possible ROC.6 Chapter 9 The Laplace Transform9.5 Properties of the Laplace Transform9.5.1 Linearity of the Laplace Transform7 Chapter 9 The Laplace Transform9.5.2 Time ShiftingExample Poles:pole-zero plot8 Chapter 9 The Laplace Transform9.5.3 Shifting in s-DomainROC的边界平移的边界平移9 Chapter 9 Th
4、e Laplace Transform9.5.4 Time Scaling When 10 Chapter 9 The Laplace Transform9.5.5 Conjugation9.5.6 Convolution Property11 Chapter 9 The Laplace Transform9.5.7 Differentiation in the Time Domain12 Chapter 9 The Laplace TransformExample Determine 139.5.8 Differentiation in the s-Domain Chapter 9 The
5、Laplace Transform14 Chapter 9 The Laplace TransformExampleDetermine Poles:15 Chapter 9 The Laplace Transform9.7 Analysis and Characterization of LTI Systems Using the Laplace TransformSystem Function or Transfer Function9.7.1 CausalityCausal 16 Chapter 9 The Laplace TransformFor a system with a rati
6、onal system function,causal9.7.2 Stability(稳定性）稳定性）Stable system:whenstableconverges17 Chapter 9 The Laplace TransformExample 9.20Causal,unstable systemnoncausal,stable systemanticausal,unstable system（反因果）（反因果）18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，且且如果如果 为有理函数为有理函数Stabi
7、lity of Causal SystemConsider the following causal systemsStable unstable 19 Chapter 9 The Laplace Transform9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations ROCA ratio of polynomials in s 20 Chapter 9 The Laplace TransformExample 9.25Consider an LTI system with i
8、nput ,Output ,determine the system function.Example Consider a causal LTI system,bunknown constantDetermine the system function and b.21 Chapter 9 The Laplace TransformThe system is unstable.22 Chapter 9 The Laplace TransformExample 9.26 An LTI system:1.The system is causal.2.is rational and has onl
9、y 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 23 Chapter 9 The Laplace TransformExample 9.27 已知一因果稳定系统，已知一因果稳定系统，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，其余零极点未知，）处没有零点，其余零极点未知，判断下列说法是否正确
10、。判断下列说法是否正确。1.的傅立叶变换收敛。的傅立叶变换收敛。在在 收敛收敛2.243.为一因果稳定系统的单位冲激响应。为一因果稳定系统的单位冲激响应。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不变不变25 Chapter 9 The Laplace Transform6.在在s=-2处有极点处有极点在在s=+2处有极点处有极点7.无法判断正确与否。无法判断正确与否。269.8 LTI 系统的方框图（信号流图）表示系统的方框图（信号流图）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
11、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,余下的子流图的特征行列式余下的子流图的特征行列式信号流图的特征行列式信号流图的特征行列式 Chapter 9 The Laplace Transform一一 Mason 增益公式增益公式27Example 9.31 Chapter 9 The Laplace Transform28 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）模拟两个基本约定：两个基本约定：1.假定所有的环路均相互接触；假定所有的环路均相互接触；2.假定每一前向通路与所有的环路相互接触；假定每一前向通路与所有的环路相互接触；29 Chapter 9 The Laplace TransformExample Consider the causal LTI system1.直接模拟直接模拟2.级联型模拟级联型模拟3.并联型模拟并联型模拟30 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 9.4531ExampleDetermine Chapter 9 The Laplace Transform32