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Concept
Chirp
Summary
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 applied to sonar, radar, and laser systems, and to other applications, such as in spread-spectrum communications (see chirp spread spectrum). This signal type is biologically inspired and occurs as a phenomenon due to dispersion (a non-linear dependence between frequency and the propagation speed of the wave components). It is usually compensated for by using a matched filter, which can be part of the propagation channel. Depending on the specific performance measure, however, there are better techniques both for radar and communication. Since it was used in radar and space, it has been adopted also for communication standards. For automotive radar applications, it is usually called linear frequency modulated waveform (LFMW).
In spread-spectrum usage, surface acoustic wave (SAW) devices 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.
The basic definitions here translate as the common physics quantities location (phase), speed (angular velocity), acceleration (chirpyness).
If a waveform is defined as:
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:
Finally, the instantaneous angular chirpyness, γ, is defined to be the second derivative of instantaneous phase or the first derivative of instantaneous angular frequency,
with the instantaneous ordinary chirpyness, c, being its normalized version:
Thus chirpyness is the rate of change of the instantaneous frequency.
Official source
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