Küpfmüller's uncertainty principle

Küpfmüller's uncertainty principle states, that the relation of the rise time of a bandlimited signal to it's bandwidth is a constant.

$\Delta f\Delta t\geq {\frac {1}{2}}$

A bandlimited signal in frequency space is given by the multiplication of any signal with a rectangular function of width $\Delta f$

$\operatorname {rect} \left({\frac {f}{\Delta f}}\right)=\chi _{[-\Delta f/2,\Delta f/2]}(f):={\begin{cases}1&|f|\leq \Delta f/2\\0&{\text{else}}\end{cases}}$

$\Delta f\Delta t\geq {\frac {1}{2}}$