Sweeping Frequency

The time-varying expression for the instantaneous frequency can be used in the original equation for a sinusoid,

$$x(t) = A\cos(2\pi f(t)t+\phi).$$

Figure 9: A chirp signal from 1 to 3 Hz.

Phase summary:

• If the instantaneous phase $\theta(t)$ is constant, the frequency is zero (DC).
• If $\theta(t)$ is linear, the frequency is fixed (constant).
• if $\theta(t)$ is quadratic, the frequency changes linearly with time.