成果信號與系統(tǒng)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: 梅森規(guī)則 （信流圖）所有環(huán)路轉移函數(shù)乘積之代數(shù)和

4、從X(s)到Y(s)之間的第k條開路的轉移函數(shù)所有兩兩不接觸環(huán)路組的轉移函數(shù)乘積之代數(shù)和所有3個互不接觸環(huán)路組的轉移函數(shù)乘積之代數(shù)和移去第k條開路后，剩下子圖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