0913 Fourier Transform of Derivative, Time Shift

또 걍 복붙. 출처

$$ f(t) = \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) \, e^{i \omega t} d\omega \\ f'(t) = \frac{d}{dt}\!\left( \frac{1}{2\pi} \int_{-\infty}^{\infty} F(\omega) \, e^{i \omega t} d\omega \right)= \frac{1}{2\pi} \int_{-\infty}^{\infty} i \omega \, F(\omega) \, e^{i \omega t} d\omega $$

따라서 \( f'(t)\)의 변환은 \(i \omega \, F(\omega)\)