- #1
Jhenrique
- 685
- 4
I never see the following hypothesis but I believe that they are true...
##\text{Re}(\hat f (\omega)) = a(\omega)##
##\text{Im}(\hat f (\omega)) = b(\omega)##
where:
##f(t) = \int_{-\infty}^{+\infty}\hat f(\omega) \exp(i \omega t) d\omega = \int_{0}^{\infty} a(\omega) \cos(\omega t) + b(\omega) \sin(\omega t) d\omega##
##\hat f (\omega) = \int_{-\infty}^{+\infty}f(t) \exp(-i \omega t) dt##
##a(\omega) = \frac{1}{\pi}\int_{-\infty}^{+\infty} f(t) \cos(\omega t) dt##
##b(\omega) = \frac{1}{\pi}\int_{-\infty}^{+\infty} f(t) \sin(\omega t) dt##
So, the two first equations are true?
##\text{Re}(\hat f (\omega)) = a(\omega)##
##\text{Im}(\hat f (\omega)) = b(\omega)##
where:
##f(t) = \int_{-\infty}^{+\infty}\hat f(\omega) \exp(i \omega t) d\omega = \int_{0}^{\infty} a(\omega) \cos(\omega t) + b(\omega) \sin(\omega t) d\omega##
##\hat f (\omega) = \int_{-\infty}^{+\infty}f(t) \exp(-i \omega t) dt##
##a(\omega) = \frac{1}{\pi}\int_{-\infty}^{+\infty} f(t) \cos(\omega t) dt##
##b(\omega) = \frac{1}{\pi}\int_{-\infty}^{+\infty} f(t) \sin(\omega t) dt##
So, the two first equations are true?
Last edited: