課件分析sigsys英才班2013-chapter9ss

1、9 The Laplace Transform 9.3 The Inverse Laplace Transform9 The Laplace TransformSoor(9.56)9 The Laplace TransformThe calculation for inverse Laplace transform:(1) Integration of complex function by equation.(2) Compute by Partial Fraction Expansion . General form of X(s):9 The Laplace TransformImpor

2、tant transform pair:The inverse Laplace transform can be determined.9 The Laplace Transform Appendix Partial Fraction ExpansionConsider a fraction polynomial:Discuss two cases of D(s)=0, for distinct root and same root.9 The Laplace Transform(1) Distinct root:thus9 The Laplace TransformCalculate A1

3、: Multiply two sides by (s-1):Let s=1, so Generally9 The Laplace Transform(2) Same root:thusFor first order poles:9 The Laplace TransformMultiply two sides by (s-1)r : For r-order poles:So 9 The Laplace Transform 9.4 The Properties of Laplace Transform (9.5)9.4.1 LinearityR1R2R1 R2IfThenNote: (1) no

4、rmally, common ROC. (2) R1 R2 may be larger than R1 or R2(9.82)9 The Laplace Transform9.4.2 Time ShiftingRIfRThen9.4.3 Shifting in s-DomainRIfThen(9.87)(9.88)R+Res0 ExampleFrom LT pairWe can get9 The Laplace Transform ExampleX(t)=?9 The Laplace Transform(1) Shifting in s-Domain(2) Shifting in time-D

5、omainSolution:From LT pair9 The Laplace TransformYou can get same x(t) by Shifting in time-Domain first.9 The Laplace Transform9.4.4 Time ScalingRIfaRThenNote:Specially,-R(9.90)(9.91) Example9 The Laplace Transform(9.14)From LT pair9.4.5 ConjugateRIfRThen(9.92)9 The Laplace Transform9.4.6 The Convol

6、ution PropertyR1R2R1 R2IfThen(9.95) ExampleNote:if R1 R2=, is not existed.9 The Laplace Transformwhere9 The Laplace TransformRes0Res09 The Laplace Transform9.4.7 Differentiation in the time DomainRRIfThen(9.98) Example9 The Laplace Transform9.4.8 Integration in the time DomainRIfThenRRes0(9.106) Example=?9 The Laplace TransformRes09 The Laplace Transform9.4.9 Differentiation in the s-DomainRRIfThen(9.100) ExampleFrom LT pair9 The Laplace Transform9.4.10 Th