# Chirp rate

Chirp rate is the instantaneous rate of change of the frequency of a waveform. If a waveform is defined as:

$x(t)=\sin\left(\phi(t)\right)$

then the instantaneous frequency is defined to be:

$f(t)=\frac{1}{2\pi} \frac{d\phi(t)}{dt}$

and the chirp rate is defined to be:

$c(t)=\frac{1}{2\pi} \frac{d^2\phi(t)}{dt^2}$

.