精品课件大学物理2(双语).ppt

zero-inputsolution零输入响应totalsolutionPhysicalsolutionlineardifferentialequationssolution1.zero-inputsolution由初始条件注：两种解法的区别，初始条件代入的先后次序不同2.zero-statesolutionHomogeneoussolution(zero-inputsolution)n阶齐次方程的解（零输入响应的求解）Therootsofthecharacteristicpolynomial求特征方程的根2.Homogeneoussolution根据特征根得值，写出零输入响应Therootsofthecharacteristicpolynomialarecallednaturalfrequencies.Thesearefrequenciesforwhichthereisanoutputintheabsenceofaninput.01代入初始值求出系数02例：47页2.3-1，50页2.3-3Theunitimpulseresponseandzero-stateresponseofsystemUnitimpulseresponseTheunitimpulseresponsegivesintuitionaboutthepropertiesofasystem.Theimpulseresponseistheresponseofasystemtounitimpulsesignal.RelationshipofH(p)h(t)UnitimpulseresponseUnitimpulseresponseWhen，theresponseistheunitimpulseresponseofsystem.①零输入响应与单位冲激响应的相同点：模式相同②不同：Ⅰ）h(t)的系数由系统微分方程决定，y(t)的系数由初始状态决定Ⅱ）h(t)中有阶跃函数，y(t)中t大于等于0，物理意义及数学表示都不同Examples:54页2.4-1，55页2.4-3，57页2.4-4Zero-stateresponseofsystemConvolutionMotivation:?ThesuperpositionintegralgivesaninsightintotheoperationofLTIsystemsthatcomplementstheinsightgivenbythetransformmethods?SolutionsofLTIsystemsinthetimedomainusingthesuperpositionintegralcangiveefficientmethodsofsolution?TheunitimpulseresponseofanLTICTsystemcharacterizethosesystemsDerivationofsuperpositionintegralWewillshowthatforaCTsystemwheref(t)isanarbitraryinput,h(t)istheunitimpulseresponse,y(t)istheoutput,andtheaboverelationiscalledthesuperpositionintegral.Why?ThesuperpositionintegralforCTsystemsGraphicviewofstaircaseapproximationtothesuperpositionintegralCTconvolution

chapter2

Time-DomainAnalysisofContinuous-TimeSignalsAndSy