Chirp (source code)
= Chirp
A <chirp> is an <oscillation> whose <instantaneous frequency> changes with <time>. For $s(t)=A\cos\phi(t)$, with a smoothly increasing <wave phase> $\phi$, the <instantaneous frequency> is $f(t)=\phi'(t)/(2\pi)$. A linear chirp has
$$
\phi(t)=2\pi\left(f_0t+\frac12\alpha t^2\right)+\phi_0,\qquad f(t)=f_0+\alpha t.
$$
The chirp rate $\alpha$ has units of <hertz> per second; positive and negative values give increasing and decreasing <frequency> over intervals where the stated interpretation applies.
A swept tone can probe the response of a <coupled oscillator> over a band, although a rapid sweep need not reproduce the steady response at each <frequency>. In <radar> or <sonar>, comparing a returned <chirp> with the transmitted signal supports <pulse compression>: a long transmitted signal can be processed into a narrow delay peak. A finite-duration <chirp> occupies a range of <frequencies>, even though its local <wave phase> supplies a well-defined instantaneous rate.
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