精品課件大學(xué)物理2(雙語(yǔ))-在線(xiàn)瀏覽
2025-07-06 15:54本頁(yè)面
【正文】 dtydtd?????不等于即 兩端積分得 )(1)(1 tfpptfpp ?????Example： Page 40 。39。 (t)+8y(t) = f(t), t ? 0 y(0)=1, y39。39。 (t)+8y(t) = 0的通解 yh(t) (unforced solution固有響應(yīng) ) yh(t) = Ae?2t+Be?4t y39。 (t)+6y39。 (2)若激勵(lì)信號(hào)發(fā)生變化，則須全部重求解。 zeroinput solution零輸入響應(yīng) linear differential equations solution Physical solution 1. zeroinput solution )()()()( tfpNtypD ??????nitixxiectytfty1)(0)()(?出特征根 根據(jù)特征方程求由初始條件 nn cccyyy ，求出， ?? ???? ,21139。 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???????????????? ?????? ① 零輸入響應(yīng)與單位沖激響應(yīng)的相同點(diǎn)：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(yè) ， 55頁(yè) ， 57頁(yè) 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 superposition integral. ? ? ? ? ? ? ??? dthfty ?? ? ??? Why? The superposition integral for CT systems Graphic view of staircase approximation to the superposition integral CT convolution )(tf )(tyDerivation of staircase approximation to superposition integral ?)(tf)( ?? ?t)()( ?? ?thf)()( ??? ?? tf)()( ?? ?ttf)(ty)()( ?? ?? thfMechanics (步驟 、 技巧 ) To pute the superposition integral ? ? ? ? ? ? ? ? ? ? ??? dthfthtfty ???? ? ???Step 1 Plot f and h vs since the convolution integral is on . Step 2 Flip h ( ? ) around the vertical axis to obtain h ( ? ) Step 3 Shift h ( ? ) by t to obtain h ( t ? ) Step 4 Multiply to obtain f ( ? ) h ( t ? ) Step 5 Integrate on ? to pute Step 6 Increase t and repeat step 3 to 6 ? ? ? ? ??? dthf ?????)(?h )(180 2 ?????? ?? ff l i p ? )())(( ?? ???????? ?? ththts hi f t CT con
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