soph2信號(hào)與系統(tǒng)同步來金梅課件

StateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei第2章連續(xù)時(shí)間系統(tǒng)的時(shí)域分微分方程式的建起始點(diǎn)的零輸入響應(yīng)和零沖激響應(yīng)和階躍卷卷積的性微分和積分設(shè)有兩個(gè)函數(shù)f1設(shè)有兩個(gè)函數(shù)f1(t)和f2(t),積f

fft 稱為f1(t)和f2(t)的卷積積分，簡(jiǎn)稱卷積，記ftftf稱為f1(t)和f2(t)的卷積積分，簡(jiǎn)稱卷積，記 StateStateKeyLabofASIC&Systems,FudanUniversity,JinmeiLinearTime-InvariantSystem:LTIS線性時(shí)不變系

系統(tǒng)在單位沖激信號(hào)(t)作用下產(chǎn)生的零狀態(tài)響應(yīng)，

d

rtethtetStateKeyLabofASIC&Systems,FudanUniversity,Jinmei借助于階躍函數(shù)u(t)確定積分利用圖解說明確定積分限StateKeyLabofASIC&Systems,FudanUniversity,Jinmei卷積的圖解f

fft 1f1(tf1(反 時(shí)2.f2(t)f2()f2()f2(t反 時(shí)3.相乘：f1(f2t4.乘積的積分 f1().f2(t)StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei

StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei四．對(duì)卷積積分rt

te()是h(t-)的，求即de()是h(t-)的，積(t-)四．對(duì)卷積積分小結(jié)（續(xù)一般數(shù)學(xué)表示：g(tf1(f2t r(t)

e()h(t)積分限 f1(t),f2(t)存在的區(qū)間決定，即f1f2t0StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmeitt2第2章連續(xù)時(shí)間系統(tǒng)的時(shí)域分卷積的性 f1(t)f2(t)f2(t)f1(tStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei

系統(tǒng)f(t)[h1(t)h2(t)]f(t)h1(t)f(t)h2(t)f(f(t)h1(tg(tf(t)h1(t)f(t)h2f(tff(tf(th2(th1(ththth

g(t

f(t)h(t

系統(tǒng)f(t)h1(t)h2(t)f(t)[h1(t)h2(t)]f(t)h(th1(th1(thth(t)

(t

g(th2(tf(t)h1(t)h2(t f

g(t

f(t)h(t)證 f1(t)f2(t)f3(t)f1(t)[f2(t)f3ff2(）f3(t(f3(tgt

f2()f3(t

)dStateKeyLabofASIC&Systems,FudanUniversity,Jinmeig(t)f(t)h(t)f(t)h(tStateKeyLabofASIC&Systems,FudanUniversity,Jinmeig(t)f(t)h(t)f(t)h(t

g(1)(t)f(t)h(1)(t)f(1)(t)hg(n)(t)f(t)h(n)(t)f(n)(t)h(tm(thn)(t)微分次數(shù)＝積分次g(nm)(t)f(n)(t)h(mm(thn)(t)微分次數(shù)＝積分次g(t)f(n)

StateKeyLabofASIC&Systems,FudanUniversity,Jinmeig(i)(t)f(j)(t)h(ij)(t)f(ij)(t)h(tdf1(t)t

f2()d

f

(t) f2(ttt

df1()dd

f2(t df1()df()

f(t)

f1()f2()StateKeyLabofASIC&Systems,FudanUniversity,Jinmei三.與沖激函數(shù)或階躍函數(shù)的卷

d

ftdff(t)(tt0)f(ttf(tt1)(tt2)f(tt1tf(t)(t)f'(ttf(t)u(t)f()df(t)k(t)fk(tf(t)k(tt0)fk(ttStateKeyLabofASIC&Systems,FudanUniversity,Jinmei舉舉StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmeixx1卷積小 第2章連續(xù)時(shí)間系統(tǒng)的時(shí)域分微分方程式的建起始點(diǎn)的零輸入響應(yīng)和零沖激響應(yīng)和階躍卷卷積的性微分和積分 積分

pt1t

StateStateKeyLabofASIC&Systems,FudanUniversity,JinmeiCdn dt

dn1r(t)dtn1

dr(t)d

r(t)

dme(t)d

Edm1e(t) d

de(t)d

整理得 (CpnCpn1 (EpmEpm1

pCn)r(t)pE p)Cpn

Cpn1 p

N(p)Epm

Epm1 p

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