Editing Chirp (section)

== Definitions ==
The basic definitions here translate as the common physics quantities location (phase), speed (angular velocity), acceleration (chirpyness).
If a [[waveform]] is defined as:
<math display="block">x(t) = \sin\left(\phi(t)\right)</math>

then the [[instantaneous angular frequency]], ''ω'', is defined as the phase rate as given by the first derivative of phase,
with the instantaneous ordinary frequency, ''f'', being its normalized version:
<math display="block">
\omega(t) = \frac{d\phi(t)}{dt}, \,
f(t) = \frac{\omega(t)}{2\pi}
</math>

Finally, the '''instantaneous angular chirpyness''' (symbol ''γ'') is defined to be the second derivative of instantaneous phase or the first derivative of instantaneous angular frequency, 
<math display="block">
\gamma(t) = \frac{d^2\phi(t)}{dt^2} = \frac{d\omega(t)}{dt}
</math>
Angular chirpyness has units of radians per square second (rad/s<sup>2</sup>); thus, it is analogous to ''[[angular acceleration]]''.

The '''instantaneous ordinary chirpyness''' (symbol ''c'') is a normalized version, defined as the rate of change of the instantaneous frequency:<ref name=Mann/>
<math display="block">
c(t) = \frac{\gamma(t)}{2\pi} = \frac{df(t)}{dt}
</math>
Ordinary chirpyness has units of square reciprocal seconds (s<sup>−2</sup>); thus, it is analogous to ''[[rotational acceleration]]''.