Chirp Signal

A chirp signal is one that sweeps linearly from a low to a high frequency.

To produce a chirping sinusoid, modifying its equation so the frequency is time-varying will likely produce better results than concatenating segments.

Recall that the original equation for a sinusoid is given by

$$x(t) = A\cos(\omega_0t+\phi)$$

where the instantaneous phase, given by $(\omega_0t+\phi)$, changes linearly with time.

Notice that the time derivative of the phase is the radian frequency of the sinusoid $\omega_0$, which in this case is a constant.

More generally, if

$$x(t) = A\cos(\theta(t)),$$

the instantaneous frequency is given by

$$\omega(t) = \frac{d}{dt}\theta(t).$$