相互相関函数のFourier変換
from フーリエ変換の諸定理
相互相関函数のFourier変換
$ \mathcal F(f\star g)(\omega)=\mathcal F(f)(\omega)^*\mathcal F(g)(\omega)
$ \mathcal F(f\star g)(\omega)=\mathcal F(f(-t)^**g(t))(\omega)
$ = \mathcal F(f(-t)^*)(\omega)\mathcal F(g)(\omega)
$ = \mathcal F(f^*)(-\omega)\mathcal F(g)(\omega)
$ \becauseF(f(at))(ω)=F(f)(ω/a)/|a|
$ = \mathcal F(f)(\omega)^*\mathcal F(g)(\omega)
$ \becauseF(f)(ω)*=F(f*)(-ω)
#2025-06-15 15:11:20