Fourier Transform 的一些重要性质的总结：
F [ α f ( t ) + β g ( t ) ] = α F ( w ) + β G ( w ) ( 1 ) \mathcal{F}[\alpha f(t) + \beta g(t)] = \alpha F(w) + \beta G(w)\quad\quad(1) F[αf(t)+βg(t)]=αF(w)+βG(w)(1)
F − 1 [ α F ( w ) + β G ( w ) ] = α f ( t ) + β g ( t ) ( 2 ) \mathcal{F}^{-1}[\alpha F(w) + \beta G(w)] = \alpha f(t) + \beta g(t)\quad\quad (2) F−1[αF(w)+βG(w)]=αf(t)+βg(t)(2)
F [ f ( t − t 0 ) ] = e − i w t 0 F ( w ) ( 3 ) \mathcal{F}[f(t-t_0)] = e^{-iwt_0}F(w)\quad\quad(3) F[f(t−t0)]=e−iwt0F(w)(3)
F − 1 [ F ( w − w 0 ) ] = e i w 0 t f ( t ) ( 4 ) \mathcal{F}^{-1}[F(w-w_0)]= e^{iw_0t}f(t)\quad\quad(4) F−1[F(w−w0)]=eiw0tf(t)(4)
F [ f ( a t ) ] = 1 ∣ a ∣ F ( w a ) ( 5 ) \mathcal{F}[f(at)] = \frac{1}{|a|}F(\frac{w}{a})\quad\quad(5) F[f(at)]=∣a∣1F(aw)(5)
F [ F ( t ) ] = 2 π f ( − w ) ( 6 ) \mathcal{F}[F(t)] = 2\pi f(-w)\quad\quad(6) F[F(t)]=2πf(−w)(6)
F [ d n ( t ) d t n ] = ( i w ) n F ( w ) ( 7 ) \mathcal{F}[\frac{d^n(t)}{dt^n}] = (iw)^nF(w)\quad\quad(7) F[dtndn(t)]=(iw)nF(w)(7)
F − 1 [ d n F ( w ) d w n ] = ( − i t ) n f ( t ) ( 8 ) \mathcal{F}^{-1}[\frac{d^nF(w)}{dw^n}] = (-it)^nf(t)\quad\quad(8) F−1[dwndnF(w)]=(−it)nf(t)(8)
g ′ ( t ) = f ( t ) , F [ f ( t ) ] = F ( w ) , F [ g ( t ) ] = 1 i w F ( w ) ( 9 ) g'(t) = f(t),\mathcal{F}[f(t)] = F(w), \mathcal{F}[g(t)] = \frac{1}{iw}F(w)\quad\quad(9) g′(t)=f(t),F[f(t)]=F(w),F[g(t)]=iw1F(w)(9)
扫一扫
被折叠的 条评论
为什么被折叠?
到【灌水乐园】发言
