Re: [理工] [工數]-反傅立葉轉換
※ 引述《Ertkkpoo (water)》之銘言:
: 各位好
: 最近算反傅立葉時遇到很大困難,就是一直不知該如何分解,套一些性質去解
: 例如說這題
: (2w-6)i
: e
: _________ 求它的反傅立葉,我有嘗試去做,但會處理積分,分子分母都有w
: 5-(3-w)i
: 的積分,但好像沒辦法用以前的微積分(ibp...)去解
exp^i(2w-6) ∞
F(w)= ____________ F{f(t)} = ∫ f(t)exp^(-iwt)dt = F(w)
5 + (w-3)i -∞
exp^i(2w)
F(w+3) = F{f(t)exp^(-i3t)} = _____________
5 + iw
-1 exp^(i2w) -1 1
f(t) = F {_____________}exp^(i3t) = F{________}︳ * exp^(i3t)
5+iw 5 + iw t→t+2
= [exp^(-5t)u(t)]︳ *exp^(i3t)
t→t+2
= exp^(-5t-10+i3t)u(t+2)
久沒轉錯了告知一下 Orz
: w是指omega也就是frequency
: 另外想問
: 我在傅立葉這裡做一些積分微分時,i可以視為常數嗎?把他提出積分符號外
: 因為n大似乎之前有問一題是找出一函數的極限,而那函數有i和cos,把i當成常數
: cosωx
: lim ──── = ?
: x→∞ iω
: 這題就會錯
: 謝謝各位
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