Chirp Totally Explained

A chirp is a signal in which the frequency increases ('up-chirp') or decreases ('down-chirp') with time. It is commonly used in sonar and radar, but has other applications, such as in spread spectrum communications. In spread spectrum usage, SAW devices such as RACs are often used to generate and demodulate the chirped signals. In optics, ultrashort laser pulses also exhibit chirp due to the dispersion of the materials they propagate through.
   In a linear chirp, the instantaneous frequency f(t ) varies linearly with time:
ť $f(t) = f_0 + k t$

where f₀ is the starting frequency (at time t = 0), and k is the rate of frequency increase or chirp rate. A corresponding time-domain function for a sinusoidal chirp is:
ť $x(t) = sin(2 pi int_0^t f(t'), dt') = sinleft(2pi (f_0 + frac$

From the equations above, it can be seen that this actually changes the rate of frequency increase of a linear chirp (kt multiplied by a constant) so that the correlation of the original function with the reflected function is low.
   Because of the geometric relationship, the Doppler shifted geometric chirp will effectively start at a different frequency (f₀ multiplied by a constant), but follow the same pattern of exponential frequency increase, so the end of the original wave, for instance, will still overlap perfectly with the beginning of the reflected wave, and the magnitude of the correlation will be high for that section of the wave.
   A chirp signal can be generated with analog circuitry via a VCO, and a linearly or exponentially ramping control voltage. It can also be generated digitally by a DSP and DAC, perhaps by varying the phase angle coefficient in the sinusoid generating function.

Chirp modulation

Chirp modulation, or linear frequency modulation for digital communication was patented by Sidney Darlingtonin 1954 with significant later work performed by Winkler in 1962. This type of modulation employs sinusoidal waveforms whose instantaneous frequency increases or decreases linearly over time. These waveforms are commonly referred to as linear chirps or simply chirps. Hence the rate at which their frequency changes is called the chirp rate. In binary chirp modulation, binary data is transmitted by mapping the bits into chirps of opposite chirp rates. For instance, over one bit period "1" is assigned a chirp with positive rate a and "0" a chirp with negative rate −a. Chirps have been heavily used in radar applications and as a result advanced sources for transmission and matched filters for reception of linear chirps are available(External Link

Chirplet transform

Another kind of chirp is the projective chirp, of the form

g = f[(acdot x + b)/(c cdot x + 1)]

, having the three parameters a (scale), b (translation), and c (chirpiness). The projective chirp is ideally suited to image processing, and forms the basis for the projective chirplet transform.

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