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拉氏变换及反变换公式拉氏变换及反变换
公式1.拉氏变换的基本性质1线性定理齐次性
叠加性L[af(t)]=aF(s)L[f1(t)±f2(t)]=F1(s)±F2(s)df(t)]360问答=sF(s)−f(0)dtd2f(t)L[]=s2
F(s)−sf(0)−f′0）（dt2⋮L[L[dnf(t
)]=snF(s)−dtndk−1f(t)f(k−1)(t)
=dtk−12微村月息东处分定理一般形式∑sk=1nn−kf(k−1)(0)初始条件为0时dnf(t)L[]=snF(节农即物层s)ndtL[∫f(t)dt]差养=F(s)[∫f(t)dt]t=0+ss2F(思溶少福古回热房s)[∫f(t)dt]t=0[∫∫f(t)(dt)]t=0+
+s2s2s一般形式3积分定理L[∫∫f(t)(dt)2]=⋮伯云茶明这银编共n个n共n个F(s)n1L[∫⋯∫f(t)(dt)]=n+∑n−k+1[∫
⋯∫f(t)(dt)n]t=0sk=1s共n个初始条件为0时45678延迟定理（或称t
域平移定理）衰减定理（或称s域平移定
理）终值定理初值定理卷积定理L[∫⋯∫f(t)(dt)n]=F(s)snL[f(t−T)1(t−T)]=e−TsF(s)L[f(t)e−at]=F(s+a)limf(t)=limsF(s)t→∞s→0limf(t)=limsF(s)t→0s→∞L[∫f1(t−τ)f2(τ)dτ]=L[∫f1(t)f2(t−τ
)dτ]=F1(s)F2(s)00tt12．常用函数的拉氏变换和z变换表序超陆超烈罗基号
拉氏变换E(s)1时首括讲于端若全见效服间函数e(t)δ(t)δT(t)=∑δ(t−nT)n=0∞Z变换E(z)1zz−112345678煤只雷运形910111213141511−e−Ts1s1她结乱危百苦照副(t)zz−11s21s3tt22Tz(z−1)2T2z(z+1)2(z−1)31sn+11s+atnn!lim(−1)n∂nz()na→0n!∂az−e−aT
zz−e−aT
标签：拉氏,计算公式,变换
