[理工] [工數]-Fourier Transform

[t5d (t5d)]

1.
x(t) = 1 ,  |t| < 1/2
x(t) = 0 ,  otherwise

         ∞
X(jw) = ∫ x(t) e^(-jwt) dt
        -∞


Find

  ∞
 ∫  |X(jw)|^2 dw  =  ?
 -∞



                           ∞
2.Let z(t) = x(t)＊y(t) = ∫ x(τ)y(t-τ)dτ
                          -∞
(a)Prove the area under z(t) is the product of the areas under x(t) and y(t)
   over the interval -∞ < t < ∞

(b)Give an interpretation

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◆ From: 125.224.82.49
※ 編輯: t5d             來自: 125.224.82.49        (03/15 11:56)
→ doom8199:1. Parseval's thm.  or  |X^2| = XX* 展開直接算
→ doom8199:2. Z(jw)=X(jw)Y(iw)  → Z(0) = X(0)Y(0)
→ doom8199:FT 在 w=0 的值，所代表的涵意就是 t-domain 下的面積
→ t5d:|X^2| = XX* 要怎麼套在這題? 不太懂@@a
→ vaNkiCk:算是定義