Dictionary:Parseval’s theorem

有兩個非周期函數h₁(t)與h₂(t), 其傅立葉變換分別為H₁(f)和 H₂(f):

$\phi _{12}(0)=\int h_{1}(t)h_{2}(t)dt=\int H_{1}(f)H_{2}(f)df=\Phi _{12}(0).$

這樣, 互相關的零延遲值₁₂(0) (左邊的兩個值) 等於叉積譜的積分; 同樣, 零頻率的互功率譜振幅Φ₁₂(0) (右邊的兩項) 等於時間域的互能量. 參照圖F-22. 由法國數學家Marc-Antoinne Parseval des Chenes (1755–1836)命名.

External links

find literature about Parseval’s theorem/zh