sinc-Funktion

\begin{aligned} \operatorname{sinc}(ax) = \frac{\sin ax}{ax} \end{aligned}

\begin{aligned} f(x) &= \begin{cases} 1 & (-\frac{b}{2} \lt x \lt \frac{b}{2}) \\ 0 & \textrm{(sonst)} \end{cases} \\ F(k) &= \int_{-\infty}^{\infty} \mathrm{e}^{-\mathrm{i}kx} f(x) \mathrm{d}x \\ &= b \operatorname{sinc} \left( \frac{bk}{2} \right) \end{aligned}