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 either orProof
A bandlimited signal with fourier transform in frequency space is given by the multiplication of any signal with with a rectangular function of width
as
Since the fourier transform of a rectangular function is a sinc function and vice versa, follows
Now the first root of is at, which is the rise time of the pulse, now follows
Equality is given as long as is finite.
Regarding that a real signal has both positive and negative frequencies of the same frequency band, becomes,
which leads to instead of
