【正文】 impulse 單位沖激信號 Unit impulse —— properties 2. 尺度變換特性 )(1)( taat ?? ?dtattg )()( ?????adxxaxgxat )()/( ??? ????ag )0(?dtattg )()( ????? ag )0(?Unit impulse 單位沖激信號 Unit impulse —— properties 3. 偶函數(shù)性 )()( tt ?? ??If a= ?1, then ?(t)=?(?t) ) / ( 1 ) ( a b t a b at ? ? ? ? ? )(1)( taat ?? ?Unit impulse 單位沖激信號 Unit impulse —— properties 4. 對時間的微分等于 單位沖激偶函數(shù) 0??0??)(t?)(39。39。39。39。d The constitutive relations for each element yield Combining KCL and the constitutive relations yields ? ????? ? t LLLLL duLitidt tdiLtu 0 )(1)0()()()( ??? ????? ? t ccccc diCutudt tduCti 0 )(1)0()()()( ??列寫電路的一般方法 ?支路電流（電壓）法 ?網(wǎng)孔分析法 ?節(jié)點電壓法 系統(tǒng)方程的算子表示方法 Operator： dttdftpfdtdpo p e r a t o ralD i f f e r e n t i )()(: ?? 　　　　　　? ??? t dftfppo p e r a t o rI n t e g r a l ?? )()(11: 　　　　)(: )(1 i n t )(: pHo p e r a t o rt r a n f e rpDo p t e r a t o re g r a ldg e n e r a l i z epNo p e r a t o rald i f f e r e n t idg e n e r a l i z e 　算子運(yùn)算規(guī)則 ? 符合代數(shù)運(yùn)算規(guī)則 例 ? ? )()23()()2)(1( 2 tfpptfpp ?????)()()()()()()()(tftytpftpyctftytfdtdtydtd?????不等于即　　兩端積分得　　　)(1)(1 tfpptfpp ?????Example： Page 40 。 (t)+8y(t) = 0的通解 yh(t) (unforced solution固有響應(yīng) ) yh(t) = Ae?2t+Be?4t y39。 h(t) )()()()( tfpktfpHty????)()()( tkftydt tdy ?? ?)()()( tfketyedttdye tttem u l t i p l y t ??? ?? ??? ?????? ?? ?tt etkftyedd ????? ?? )()]([? ?? ?? ??? ?? tto dfekye 0i n t e g r a l )()( ??? ????? ? ??? t tf dfekty 0 )( )()( ????? ? ?? ??? t tt dfekeyty 0 )( )()0()( ?????Unit impulse response When ， the response is the unit impulse response of system. )()( ttf ??)()()()(00)(tkedekedekthtttt t???????????????? ??????　　?、?零輸入響應(yīng)與單位沖激響應(yīng)的相同點：模式相同 ②不同： Ⅰ ） h(t)的系數(shù)由系統(tǒng)微分方程決定， y(t)的系數(shù)由初始狀態(tài)決定 Ⅱ ） h(t)中有階躍函數(shù)， y(t)中 t大于等于 0， 物理意義及數(shù)學(xué)表示都不同 Examples: 54頁 ， 55頁 ， 57頁 Unit impulse response Zerostate response of system )()()()()()()()()(.100)(tfthdfthtytkethdfektytftttf????????????????????　Convolution ? ??? ??? ??? dtfftftf )()()()( 2121Motivation: ? The superposition integral gives an insight into the operation of LTI systems that plements the insight given by the transform methods ? Solutions of LTI systems in the time domain using the superposition integral can give efficient methods of solution ? The unit impulse response of an LTI CT system characterize those systems Derivation of superposition integral We will show that for a CT system where f ( t ) is an arbitrary input, h ( t ) is the unit impulse response, y ( t ) is the output, and the above relation is called the