Chirp
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A chirp is a
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.
Definitions
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
Finally, the instantaneous angular chirpyness (symbol γ) is defined to be the second derivative of instantaneous phase or the first derivative of instantaneous angular frequency,
The instantaneous ordinary chirpyness (symbol c) is a normalized version, defined as the rate of change of the instantaneous frequency:[3]
Types
Linear
In a linear-frequency chirp or simply linear chirp, the instantaneous frequency varies exactly linearly with time:
Here, is the final frequency and is the time it takes to sweep from to .
The corresponding time-domain function for the phase of any oscillating signal is the integral of the frequency function, as one expects the phase to grow like , i.e., that the derivative of the phase is the angular frequency .
For the linear chirp, this results in:
where is the initial phase (at time ). Thus this is also called a quadratic-phase signal.[4]
The corresponding time-domain function for a
Exponential
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, and , and the time interval between them is kept constant, the frequency ratio will also be constant.[5][6]
In an exponential chirp, the frequency of the signal varies exponentially as a function of time:
The corresponding time-domain function for the phase of an exponential chirp is the integral of the frequency:
The corresponding time-domain function for a sinusoidal exponential chirp is the sine of the phase in radians:
As was the case for the Linear Chirp, the instantaneous frequency of the Exponential Chirp consists of the fundamental frequency accompanied by additional
Hyperbolic
Hyperbolic chirps are used in radar applications, as they show maximum matched filter response after being distorted by the Doppler effect.[7]
In a hyperbolic chirp, the frequency of the signal varies hyperbolically as a function of time:
The corresponding time-domain function for the phase of an hyperbolic chirp is the integral of the frequency:
The corresponding time-domain function for a sinusoidal hyperbolic chirp is the sine of the phase in radians:
Generation
A chirp signal can be generated with
Relation to an impulse signal
A chirp signal shares the same spectral content with an
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 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.
Chirplet transform
Another kind of chirp is the projective chirp, of the form:
Key chirp
A change in frequency of
See also
- Chirp spectrum - Analysis of the frequency spectrum of chirp signals
- Chirp compression - Further information on compression techniques
- Chirp spread spectrum - A part of the wireless telecommunications standard IEEE 802.15.4a CSS
- Chirped mirror
- Chirped pulse amplification
- Chirplet transform - A signal representation based on a family of localized chirp functions.
- Continuous-wave radar
- Dispersion (optics)
- Pulse compression
- Radio propagation § Measuring HF propagation
References
- ^ Weisstein, Eric W. "Sweep Signal". From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SweepSignal.html
- S2CID 41233620.
- ^ a b Mann, Steve and Haykin, Simon; The Chirplet Transform: A generalization of Gabor's Logon Transform; Vision Interface '91.[1]
- ISBN 9781119991861. Retrieved 2014-12-03.
- ^ Li, X. (2022-11-15), Time and Frequency Analysis Methods on GW Signals, retrieved 2023-02-10
- PMID 18334358.
- S2CID 16476642.
- ^ "Chirp Signal - an overview | ScienceDirect Topics". www.sciencedirect.com. Retrieved 2023-02-10.
- S2CID 206870096.
- ^ "Chirped pulses". setiathome.berkeley.edu. Retrieved 2014-12-03.
- ISBN 9781119991861. Retrieved 2014-12-03.
- ^ a b "Chirp Signals". dspguide.com. Retrieved 2014-12-03.
- ^ arXiv:1907.04186 [eess.SP].
- ^ The Beginner's Handbook of Amateur Radio By Clay Laster
External links
- Online Chirp Tone Generator (WAV file output)
- CHIRP Sonar on FishFinder
- CHIRP Sonar on FishFinder