A chirp is a signal (information theory) 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 Weisstein, Eric W. "Sweep Signal." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SweepSignal.html 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 devices such as reflective array compressor are often used to generate and demodulate the chirped signals. In optics ultrashort pulse laser pulses also exhibit chirp due to the dispersion (optics) of the materials they propagate through.

Types of chirp

Linear chirp

In a linearchirp, the instantaneous phase#Instantaneous frequency ft) varies linearly with time: :$f(t)\; f\_0\; +\; k\; t$ where flt;sub>0 is the starting frequency (at time t 0), and kis the rate of frequency increase or chirp rate The corresponding time-domain function for a sinusoidal linear chirp is: :$x(t)\; \backslash sin\backslash left2\; \backslash pi\; \backslash int\_0^t\; f(t)\backslash ,\; dt\backslash right]\; \backslash sin\backslash left2\; \backslash pi\; \backslash int\_0^t\; (f\_0\; +\; k\; t)\backslash ,\; dt\backslash right]\; \backslash sin\backslash left2\backslash pi\; (f\_0\; +\; \backslash frack\}2\}\; t)\; t\; \backslash right]$ File:Linear-chirp.svg Image:LinearChirp.jpg of a Linear Chirp. The Spectrogram plot demonstrates the linear rate of change in frequency as a function of time, in this case from 0 to 7 kHz repeating every 2.3 seconds. The intensity of the plot is proportional to the energy content in the signal at the indicated frequency and time.]] In the frequency domain, the instantaneous frequency described by the equation $f(t)\; f\_0\; +\; k\; t$ 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 progression relationship over time. In other words, if two points in the waveform are chosen, tlt;sub>1 and tlt;sub>2, and the time interval between them tlt;sub>2 − tlt;sub>1 is kept constant, the frequency ratio ftlt;sub>2)/ftlt;sub>1) will also be constant. In an exponentialchirp, the frequency of the signal varies exponential function as a function of time: :$f(t)\; f\_0\; k^t$ where flt;sub>0 is the starting frequency (at t 0), and kis the rate of exponential growth in frequency. Unlike the linear chirp, which has a constant chirp rate, an exponential chirp has an exponentially increasing chirp rate. The corresponding time-domain function for a sinusoidal exponential chirp is: :$x(t)\; \backslash sin\backslash left2\; \backslash pi\; \backslash int\_0^t\; f(t)\backslash ,\; dt\backslash right]\; \backslash sin\backslash left2\; \backslash pi\; f\_0\; \backslash int\_0^t\; k^t\}\; dt\backslash right]\; \backslash sin\backslash left2\backslash pi\; f\_0\; \backslash frack^t\; -\; 1\}\backslash ln(k)\}\backslash right]$ File:exponentialchirp.png Image:Expchirp.jpg of an exponential chirp. The exponential rate of change of frequency is shown as a function of time, in this case from 0 to 8 kHz repeating every second. Also visible in this Spectrogram is a frequency fallback to 6 kHz after peaking, likely an artifact of the specific method employed to generate the waveform.]] As was the case for the Linear Chirp, the instantaneous frequency of the Exponential Chirp consists of the fundamental frequency $f(t)\; f\_0\; k^t$ accompanied by additional harmonics Although somewhat harder to generate, a geometric chirp does not suffer from reduction in correlation gain if the echo is Doppler effect shifted by a moving target. This is because the Doppler shift actually scalesthe frequencies of a wave by a multiplier (shown below as the constant c. :$f(t)\_\backslash mathrmDoppler\}\}\; c\; f(t)\_\backslash mathrmOriginal\}\}$ From the equations above, it can be seen that this actually changes the rate of frequency increase of a linear chirp (ktmultiplied 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 (flt;sub>0 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 circuit y via a voltage-controlled oscillator and a linearly or exponentially ramping control voltage It can also be generated digital y by a digital signal processor and digital to analog converter perhaps by varying the phase angle coefficient in the sinusoid generating function.

Uses and occurrences

Chirp modulation

Chirp modulation, or linear frequency modulation for digital communication was patented by Sidney Darlington in 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 aand "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.http://www.stanford.edu/~hengstle/References/Reference_5.pdf File:P-type-chirplets-for-image-processing.png

Chirplet transform

Another kind of chirp is the projective chirp, of the form $\backslash scriptstyle\; g\; f\backslash left\backslash fraca\; \backslash cdot\; x\; +\; b\}c\; \backslash cdot\; x\; +\; 1\}\backslash right]$, 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

Key chirp

A change in frequency of Morse code from the desired frequency, due to poor stability in the Radio frequency Oscillator is known as chirp The Beginners Handbook of Amateur Radio By Clay Laster and in the RST code is given an appended letter C.

See also

* Chirplet transform - A signal representation based on a family of localized chirp functions, each member of which can usually be expressed as parameterized transformations of each other. * Pulse compression - A signal processing technique designed to maximize the sensitivity and resolution of radar systems by modifying transmitted pulses to improve their auto-correlation properties. One way of accomplishing this is to chirp the RADAR signal (also known as Chirp Radar . * Chirp Spread Spectrum - A part of the wireless telecommunications standard IEEE 802.15.4a CSS (see http://www.ieee802.org/15/pub/05/15-05-0002-00-004a-nanotron-chirp-spread-spectrum-css-phy-presentation.ppt Chirp Spread Spectrum (CSS) PHY Presentation for IEEE P802.15.4a]). * Continuous-wave radar * SHARAD * Chirped pulse amplification * Chirped mirror * Dispersion (optics)

References

Category:Signal processing ca:Freqüència modulada polsada de:Chirp es:Frecuencia modulada pulsada fr:Chirp it:Chirp pl:Radar impulsowy ru:Линейная частотная модуляция