Küpfmüller's uncertainty principle

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

with ${\displaystyle k}$ either ${\displaystyle 1}$ or ${\displaystyle {\frac {1}{2}}}$

A bandlimited signal ${\displaystyle u(t)}$ with fourier transform ${\displaystyle {\hat {u}}(f)}$ in frequency space is given by the multiplication of any signal ${\displaystyle {\underline {\hat {u}}}(f)}$ with ${\displaystyle {\hat {u}}(f)={{\underline {\hat {u}}}(f)}{{\Big |}_{\Delta f}}}$ with a rectangular function of width ${\displaystyle \Delta f}$

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