| \( f(t) \) | \( F(\omega) \) |
| \( u(t) e^{-a t} \), \( a > 0 \) | \( \dfrac{1}{a + j \omega} \) |
| \( f(t) = 1 \) für \( -a \leq t \leq a \) und \( 0 \) sonst |
\( \dfrac{2 \sin (\omega a)}{\omega} \) |
| \( f(t) = A \) (Konstante) | \( 2 \pi A \delta (\omega) \) |
| \( \delta (t) \) | 1 |
| \( \delta (t - a) \) | \( e^{-j \omega a} \) |
| \( \cos (a t) \) | \( \pi [\delta (\omega + a) + \delta (\omega - a)] \) |
| \( \sin (a t) \) | \( -j \pi [\delta (\omega - a) - \delta (\omega + a)] \) |
| \( e^{j a t} \) | \( 2 \pi [\delta (\omega - a)] \) |
| \( f'(t) \) | \( j \omega F(\omega) \) |
| \( f''(t) \) | \( (j \omega)^2 F(\omega) \) |
| \( t f(t) \) | \( j \dfrac{d F(\omega)}{d \omega} \) |
| \( t^2 f(t) \) | \( j^2 \dfrac{d^2 F(\omega)}{d \omega^2} \) |