文稿分析sigsys英才班2013-chapter9ss l

1、9 The Laplace Transform9.7 System Function Algebra and Block Diagram Representations (9.8)9.7.1 System Functions for Interconnections of LTI SystemsParallelSeries(cascade)9 The Laplace TransformFeed-back9.7.2 Block Diagram Representation for causal LTI Systems Described by Differential Equations and

2、 Rational System Functions adderBasic elements:adder;multiplication by a coefficient; integrator9 The Laplace Transformmultiplicationintegrator9 The Laplace TransformExample 9.28LetThen,9 The Laplace TransformEquivalent representation9 The Laplace TransformExample 9.29(9.164)Let9 The Laplace Transfo

3、rmcannonic form:the number of integrator =the order of differential equation9 The Laplace TransformExample 9.30LetThen,(1) direct-form9 The Laplace Transform9 The Laplace Transform(2) cascade-form9 The Laplace Transform(3) parallel-formPartial Fraction Expansion9 The Laplace TransformExample 9.31Let

4、9 The Laplace TransformLetThen,9 The Laplace TransformState Equation from block-diagram9 The Laplace TransformExample 9.31s-domaint-domainState variable9 The Laplace TransformState Equations-domaint-domainwhere9 The Laplace TransformCould you get equations from other forms of block-diagram?Output Eq

5、uationt-domainHow to solute state equations in s- or t-domain ?Read references by yourself!s-domain9 The Laplace Transform9.8 The Unilateral LT(9.9)or Res 1The most properties of Unilateral LT are same as LT,except differentiation and integration in the time Domain.9 The Laplace TransformDifferentia

6、tion in the time Domainintegration in the time Domain (appended)Res 11. It is very useful to solving a differential equation with nonzero initial conditions9 The Laplace TransformApplications of Unilateral LTExample9 The Laplace Transform(9.197)Using Unilateral LT9 The Laplace TransformIf 9 The Laplace Transform2. It is also useful to solving a circuit with nonzero initial conditions9 The Laplace Transform9 The Laplace TransformExample9 The Laplace TransformYou can get Inverse LT, Resume of Charpter 9h(t)H(s)x(t)y(t)=x(t)*h(t)X(s)Y(s)=X(s)H(s)Properties and Basic LT Pairs(ROC)Key points of a