Chirp

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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.[1] 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.

Contents

Types of chirp

Linear chirp

In a linear chirp, the instantaneous frequency f(t ) varies linearly with time:

where f0 is the starting frequency (at time t = 0), and k is the rate of frequency increase or chirp rate. The corresponding time-domain function for a sinusoidal linear chirp is:

In the frequency domain, the instantaneous frequency described by the equation f(t) = f0 + kt is accompanied by additional frequencies (harmonics) which exist as a fundamental consequence of Frequency Modulation. These harmonics are quantifiably described through the use of Bessel Functions. However with the aid of Frequency vs. Time profile Spectrogram one can readily see that the linear chirp has spectral components at harmonics of the fundamental chirp.

Exponential chirp

In a geometric chirp, also called an exponential chirp, the frequency of the signal varies with a geometric relationship over time. In other words, if two points in the waveform are chosen, t1 and t2, and the time interval between them t2t1 is kept constant, the frequency ratio f(t2)/f(t1) will also be constant.

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