soph2信号与系统同步来金梅课件

StateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei第2章连续时间系统的时域分微分方程式的建起始点的零输入响应和零冲激响应和阶跃卷卷积的性微分和积分设有两个函数f1设有两个函数f1(t)和f2(t),积f

fft 称为f1(t)和f2(t)的卷积积分，简称卷积，记ftftf称为f1(t)和f2(t)的卷积积分，简称卷积，记 StateStateKeyLabofASIC&Systems,FudanUniversity,JinmeiLinearTime-InvariantSystem:LTIS线性时不变系

系统在单位冲激信号(t)作用下产生的零状态响应，

d

rtethtetStateKeyLabofASIC&Systems,FudanUniversity,Jinmei借助于阶跃函数u(t)确定积分利用图解说明确定积分限StateKeyLabofASIC&Systems,FudanUniversity,Jinmei卷积的图解f

fft 1f1(tf1(反 时2.f2(t)f2()f2()f2(t反 时3.相乘：f1(f2t4.乘积的积分 f1().f2(t)StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei

StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei四．对卷积积分rt

te()是h(t-)的，求即de()是h(t-)的，积(t-)四．对卷积积分小结（续一般数学表示：g(tf1(f2t r(t)

e()h(t)积分限 f1(t),f2(t)存在的区间决定，即f1f2t0StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmeitt2第2章连续时间系统的时域分卷积的性 f1(t)f2(t)f2(t)f1(tStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmei

系统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

系统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)证 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)微分次数＝积分次g(nm)(t)f(n)(t)h(mm(thn)(t)微分次数＝积分次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.与冲激函数或阶跃函数的卷

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举举StateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateKeyLabofASIC&Systems,FudanUniversity,JinmeiStateStateKeyLabofASIC&Systems,FudanUniversity,Jinmeixx1卷积小 第2章连续时间系统的时域分微分方程式的建起始点的零输入响应和零冲激响应和阶跃卷卷积的性微分和积分 积分

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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