Chirpyness

A chirp is a signal in which the frequency increases (up-chirp) or decreases (down-chirp) with time. In some sources, the term chirp is used interchangeably with sweep signal. It is commonly used in sonar and radar, but has other applications, such as in spread-spectrum communications. In spread-spectrum usage, surface acoustic wave (SAW) devices such as reflective array compressors (RACs) are often used to generate and demodulate the chirped signals. In optics, ultrashort laser pulses also exhibit chirp, which, in optical transmission systems, interacts with the dispersion properties of the materials, increasing or decreasing total pulse dispersion as the signal propagates. The name is a reference to the chirping sound made by birds; see bird vocalization.

If a waveform is defined as:

then the instantaneous frequency is defined to be the phase rate:

and the (instantaneous) chirpyness is defined to be the frequency rate:

In a linear chirp, the instantaneous frequency ${\displaystyle f(t)}$ varies exactly linearly with time:

where ${\displaystyle f_{0}}$ is the starting frequency (at time ${\displaystyle t=0}$), and ${\displaystyle k}$ is the rate of frequency change or chirpyness.

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