Re: [理工] [工數]-摺積
※ 引述《SS327 (土豆人)》之銘言：
: http://tinyurl.com/7sjksce
: 第6題..如果是0~無限大可以先取拉式後在反拉
: 但是負無限大~正無限大可以先取傅立葉轉換，再取逆轉換嗎??
: 解答把負無限大~正無限大分段來做...看不懂他他計算過程...
: 請問一下這一類2個函數區間都在無限大的摺積要怎麼做啊??
f(t) * g(t)
t-1 -|τ|
= ∫ e * 1 dτ
t+1
If t+1 < 0
t-1 τ τ｜t-1 t -1
原式 = ∫ e dτ = e ｜ = e (e - e)
t+1 ｜t+1
If t-1 < 0 < t+1
0 -τ t-1 τ -τ｜t+1 τ｜t-1 -1 t -t
原式 = ∫ e dτ + ∫ e dτ = e ｜ + e ｜ = e (e + e ) - 2
t+1 0 ｜0 ｜0
If t-1 > 0
t-1 -τ -τ｜t+1 -t -1
原式 = ∫ e dτ = e ｜ = e (e - e)
t+1 ｜t-1
-1 t -t
｛ e (e + e ) - 2 , -1 ≦ t ≦ 1
｛
=> f(t) * g(t) = ｛
｛ -|t| -1
｛ e (e - e) , |t| > 1
第二小題叫你找 Fourier Transform 就是證明這兩個做出來結果會一樣
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