成果信号与系统chapter9-6the laplace transform

1、Chapter 9The Laplace Transform- Block Diagram Representations - The Unilateral LT9.8 System Function Algebra and Block Diagram Representations9.8.1 System Functions for Interconnections of LTI SystemsParallelR1R2Series(cascade)()(1)()(211sHsHsHsH+=Feed-backR1R2E(s)(1sH)(2sH)(sX)(sYR1R2Y(s)=H1(s)E(s)

2、E(s)=X(s)-H2(s)Y(s)9.7.2 Block Diagram Representation for causal LTI Systems Described by Differential Equations and Rational System Functions Basic elements:addermultiplicationby a coefficientintegratorExample 9.28LetThen,We can describe the system asEquivalent representation3-)(sX)(sY)(sEs1s13)(sX

3、)(sY)(sEExample 9.29LetNote: the number of integrator = the order of differential equationcanonicExample 9.30LetThen,(1) direct-forms1)(sX)(sY)(sE)(sFs13-2-s11-)(sX)(1sE)(1sY(2) cascade-forms12-)(2sE)(sY(3) parallel-formExample 9.31LetLetThen,Homework: 9.35 9.37(a)*Appendix: 梅森规则 （信流图）所有环路转移函数乘积之代数和

4、从X(s)到Y(s)之间的第k条开路的转移函数所有两两不接触环路组的转移函数乘积之代数和所有3个互不接触环路组的转移函数乘积之代数和移去第k条开路后，剩下子图的行列式梅森行列式X(s)Y(s)H(s)X(s)Y(s)H(s)Definition: Res19.9 The Unilateral LTTHE tool to analyze causal CT systems described by LCCDEs with initial conditionsThat imply:If x(t)=x(t)u(t), Examples 12According to the Res-2Why?Properties of the Unilateral LTsee table 9.3 Page 717 The most properties of Unilateral LT are same as LT except differentiation and integration in the time Domain.Differentiation Property for ULTDerivation:Note:ExampleSolutionObviously, Using Unilateral LTExampl