Chirp

Chirp is a redirect to this article. For the chirp as an insect see " Cicadas ".

Chirp pulse with linear frequency increase

Audio example: Locating calls from a pipistrelle bat , playback slowed down 20 times.
At the beginning of the recording, the calls begin with a chirp that begins at around 70 kHz and drops to 46 kHz in a few milliseconds. The total duration of a call is approx. 15 milliseconds.

As a chirp ( English (to) chirp "chirp, chirp, chirping ") or a cicada is in the signal processing means a signal whose frequency varies with time. A distinction is made between positive chirps - in which the frequency increases over time - and negative [chirps] - in which the frequency decreases .

Technical applications are in the transmission of microwaves with the synthetic aperture radar and with band-spreading modulation methods such as chirp spread spectrum (CSS). In nature, bats use chirp pulses to locate them .

Strong, short laser pulses are "chirped" in order to be able to amplify them with a longer pulse duration ( chirped pulse amplification ).

Chirp description

A typical example is a signal with the following timing: ${\displaystyle x(t)}$

${\displaystyle x(t)=\sin \left(2\pi \int f(\tau )\mathrm {d} \tau \right)\,}$

In this case it is interpreted as a time-dependent frequency, for the indeterminate integral a concrete fixed antiderivative of is to be used. This interpretation requires a more precise explanation, because according to the uncertainty principle of the Fourier transformation (see also Heisenberg's uncertainty principle ) it is not possible to determine the point in time and frequency together exactly. ${\displaystyle f(t)}$ ${\displaystyle f(t)}$

The frequency specification is to be understood in such a way that approximately full periods of the sine are run through in a time interval, i.e. the average frequency is. According to the mean value theorem of integral calculus, there is at least one point in time at which this value also assumes. In order to speak of an instantaneous frequency, the time interval should encompass several full periods, but the change in in this interval should be small, so that the mean frequency is always close to the value of . ${\displaystyle [t_{a},t_{e}]}$ ${\displaystyle \textstyle \int _{t_{a}}^{t_{e}}f(\tau )\mathrm {d} \tau }$ ${\displaystyle \textstyle {\frac {1}{t_{e}-t_{a}}}\int _{t_{a}}^{t_{e}}f(\tau )\mathrm {d} \tau }$ ${\displaystyle \textstyle t_{m}\in (t_{a},t_{e})}$ ${\displaystyle f(t_{m})}$ ${\displaystyle f(t)}$ ${\displaystyle f(t)}$

Examples and Applications

Reduction of the pulse power with radar

Pulse compression with a SAW filter

In order to hear radar responses of distant reflexes from the noise, a certain minimum energy must be received. For exact distance measurements one needs the shortest possible transmission pulses, because with a 0.1 µs short transmission pulse the wave packet is already 30 m long. The combination of both requirements leads to immense transmission powers of 10 MW, the generation of which in aircraft or satellites causes problems. As a solution, a low-performance chirp pulse with a longer overall duration is sent with the pulse compression method , which is compressed into a considerably shorter pulse when received by special filters or mathematical processes. This can then be easily discovered in the noise.

Linear chirp

For the special case of a linear chirp, the frequency increases linearly with the constant : ${\displaystyle k}$

${\displaystyle f(t)=f_{0}+kt\,}$

and it applies to the passage of time : ${\displaystyle x(t)}$

${\displaystyle x(t)=\sin \left(2\pi \int _{0}^{t}f(\tau )\,\mathrm {d} \tau \right)=\sin \left(2\pi \int _{0}^{t}(f_{0}+k\tau )\,\mathrm {d} \tau \right)=\sin \left(2\pi \left(f_{0}+{\frac {k}{2}}t\right)t\right)\,.}$

Acoustic example: linear chirp (5 repetitions) ^{? / i}

Exponential chirp

Chirp pulse with exponential increase in frequency

Exponential chirps are often used for radar or sonar . Here the frequency dependence on the time, if the fixed fundamental frequency is and a constant: ${\displaystyle f_{0}}$ ${\displaystyle k}$

${\displaystyle f(t)=f_{0}k^{t}=f_{0}e^{t\ln(k)}}$

and thus the passage of time : ${\displaystyle x(t)}$

${\displaystyle x(t)=\sin \left(2\pi \int _{0}^{t}f(\tau )\,\mathrm {d} \tau \right)=\sin \left(2\pi f_{0}\int _{0}^{t}e^{\tau \ln(k)}\mathrm {d} \tau \right)=\sin \left({\frac {2\pi f_{0}}{\ln(k)}}\left(k^{t}-1\right)\right)\,.}$

Acoustic example: exponential chirp (5 repetitions) ^{? / i}

Gravity

In a more general definition, a chirp has the shape

${\displaystyle x(t)=|t|^{a}\sin \left(2\pi t^{-b}\right)\,,}$

with the parameters and . This type of signal occurs in practice when detecting gravitational waves . ${\displaystyle a}$ ${\displaystyle b}$

Dispersion in light

In optics, light pulses are distorted by a wavelength-dependent refractive index , the so-called dispersion :

${\displaystyle n(\lambda )=n_{0}+n_{1}\lambda +n_{2}\lambda ^{2}+\dots \quad }$ With ${\displaystyle \quad n_{i}={\partial ^{(i)}n(\lambda ) \over \partial \lambda ^{i}}\,.}$

When generating and transmitting ultra-short light pulses, it is necessary to compensate for this phase shift. In addition to prisms, so-called chirped mirrors are used, which are able to compress extended and distorted pulses again due to a frequency-dependent reflection .

The mostly undesired laser chirp occurs with the direct modulation of semiconductor lasers, see Distributed Feedback Laser

Application sonar

In order to detect the water depth and fish by means of sonar , devices have been available since at least 2015 whose sound impulses (pings) not only use several discrete fixed frequencies in the usable ultrasonic spectrum of 28–235 kHz , but typically wipe through 3 areas of this spectrum. The lower of three frequency ranges extends from 28 to 65 or 70 kHz. The highest penetration depth in water (but low angular resolution) is achieved at the lower end of the range;

Compressed High Intensity Radiated Pulse was invented as a backronym for CHIRP .

Web links

Commons : Chirp  - collection of images, videos and audio files

Others

Garmin Chirp is a small radio module that communicates with compatible Garmin navigation devices to indicate a nearby geocache with additional information, to count visitors and to display this number to the owner of the Chirp when approaching.

Chirp is the name of free software that can be used to program amateur radios from many manufacturers with a wide variety of data formats as input.

Individual evidence

1. ↑ Ryan Moody Fishing: Garmin CHIRP technology compared to traditional fish finding sonar youtube.com, June 20, 2015, accessed July 18, 2017. - Video (8:24), English
2. ↑ 2: 38/8: 24 of the youtube video.
3. ↑ Garmin Chirp trekkinn.com, accessed July 18, 2017.
4. ↑ Chirp Homepage chirp.danplanet.com, accessed on October 26, 2018.