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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. It is commonly used in sonar, radar, and laser, but has other applications, such as in spread-spectrum communications. 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, radar, and laser, but has other applications, such as in spread-spectrum communications. 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. 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. In a linear-frequency chirp or simply linear chirp, the instantaneous frequency f ( t ) {displaystyle f(t)} varies exactly linearly with time: where f 0 {displaystyle f_{0}} is the starting frequency (at time t = 0 {displaystyle t=0} ), and c {displaystyle c} is the chirpyness, assumed constant: where f 1 {displaystyle f_{1}} is the final frequency; T {displaystyle T} is the time it takes to sweep from f 0 {displaystyle f_{0}} to f 1 {displaystyle f_{1}} .

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