# Rapid changes in signal correspond to high frequencies - proof

If I consider a generic aperiodic signal $x(t)$, how can I prove that rapid changes in signal correspond to high frequencies?

• The amplitude of the first derivative of a sinusoid of frequency $f$ Hz is proportional to $f$. This makes sense; if the period repeats more quickly, it has to change at a faster rate. – Jason R Sep 1 '17 at 22:32
One might argue that the Dirac delta $\delta(t)$ , is a signal that exhibits maximum change because all frequencies are uniformly increased, not just the high frequencies