A chirp is a signal In the fields of communications, signal processing, and in electrical engineering more generally, a signal is any time-varying or spatial-varying quantity in which the frequency Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency increases ('up-chirp') or decreases ('down-chirp') with time. It is commonly used in sonar Sonar is a technique that uses sound propagation (usually underwater) to navigate, communicate with or detect other vessels. There are two kinds of sonar: active and passive. Sonar may be used as a means of acoustic location and of measurement of the echo characteristics of "targets" in the water. Acoustic location in air was used before and radar Radar is an object detection system that uses electromagnetic waves to identify the range, altitude, direction, or speed of both moving and fixed objects such as aircraft, ships, motor vehicles, weather formations, and terrain. The term RADAR was coined in 1941 as an acronym for radio detection and ranging. The term has since entered the English, but has other applications, such as in spread spectrum Spread-spectrum techniques are methods by which electromagnetic energy generated in a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth. These techniques are used for a variety of reasons, including the establishment of secure communications, increasing resistance to natural communications. In spread spectrum usage, SAW A surface acoustic wave is an acoustic wave traveling along the surface of a material exhibiting elasticity, with an amplitude that typically decays exponentially with depth into the substrate devices such as RACs are often used to generate and demodulate the chirped signals. In optics Optics is the study of the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays,, ultrashort In optics, an ultrashort pulse of light is an electromagnetic pulse whose time duration is on the order of the femtosecond . Such pulses have a broadband optical spectrum, and can be created by mode-locked oscillators. They are commonly referred to as ultrafast events laser A laser is a device that emits light through a process called stimulated emission. The term laser is an acronym for light amplification by stimulated emission of radiation. Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical pulses also exhibit chirp due to the dispersion In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency. Media having such a property are termed dispersive media. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity of the materials they propagate through.

Types of chirp

Linear chirp

In a linear chirp, the instantaneous frequency When is constrained to an interval such as or it is called the wrapped phase. Otherwise it is called unwrapped, which is a continuous function of argument assuming is a continuous function of Unless otherwise indicated, the continuous form should be inferred f(t ) varies linearly with time:

f(t) = f₀ + kt

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 The sine wave or sinusoid is a function that occurs often in mathematics, music, physics, signal processing, audition, electrical engineering, and many other fields. Its most basic form is: linear chirp is:

Exponential chirp

In a geometric chirp, also called an exponential chirp, the frequency of the signal varies with a geometric In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, .. relationship over time. In other words, if two points in the waveform are chosen, t₁ and t₂, and the time interval between them t₂ − t₁ is kept constant, the frequency ratio f(t₂)/f(t₁) will also be constant.

In an exponential chirp, the frequency of the signal varies exponentially The exponential function is a function in mathematics that produces as its output the exponentiation of Euler's number by a real input variable. The application of this function to a value x is written as exp(x). Equivalently, this can be written in the form ex, where e is the mathematical constant that is the base of the natural logarithm ( as a function of time:

f(t) = f₀k^t

where f₀ is the starting frequency (at t = 0), and k is the rate of exponential increase Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value. In the case of a discrete domain of definition with equal intervals it is also called geometric growth or geometric decay (the function values form a geometric progression) 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:

Although somewhat harder to generate, a geometric chirp does not suffer from reduction in correlation In statistics, correlation indicates the strength and direction of a linear relationship between two random variables. That is in contrast with the usage of the term in colloquial speech, which denotes any relationship, not necessarily linear. In general statistical usage, correlation or co-relation refers to the departure of two random variables gain if the echo is Doppler The Doppler effect , named after Austrian physicist Christian Doppler who proposed it in 1842, is the change in frequency of a wave for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is increased (compared to the-shifted by a moving target. This is because the Doppler shift actually scales the frequencies of a wave by a multiplier (shown below as the constant c).

f(t)_Doppler = cf(t)_Original

From the equations above, it can be seen that this actually changes the rate of frequency increase of a linear chirp (kt multiplied 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 (f₀ 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 circuitry Analogue electronics are those electronic systems with a continuously variable signal. In contrast, in digital electronics signals usually take only two different levels. The term "analogue" describes the proportional relationship between a signal and a voltage or current that represented the signal via a VCO A voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase modulation (PM); a VCO with digital pulse output may, and a linearly or exponentially ramping control voltage Voltage is commonly used as a short name for electrical potential difference. In this introduction, the term "voltage" is however used to mean electric potential, i.e. a hypothetically measurable physical dimension, and is denoted by the algebraic variable V . The SI unit for voltage is the volt (symbol: V [not italicized]). Note that. It can also be generated digitally A digital system is a data technology that uses discrete values represented by high and low states known as bits. By contrast, non-digital (or analog) systems use a continuous range of values to represent information. Although digital representations are discrete, the information represented can be either discrete, such as numbers, letters or by a DSP Digital signal processing algorithms typically require a large number of mathematical operations to be performed quickly on a set of data. Signals are converted from analog to digital, manipulated digitally, and then converted again to analog form, as diagrammed below. Many DSP applications have constraints on latency; that is, for the system to and DAC In electronics, a digital-to-analog converter is a device for converting a digital (usually binary) code to an analog signal (current, voltage or electric charge), 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 Sidney Darlington was an electrical engineer and inventor of a transistor configuration in 1953, the Darlington pair. He advanced the state of network theory, developing the insertion-loss synthesis approach, and invented chirp radar, bombsights, and gun and rocket guidance 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[1].

Chirplet transform

Another kind of chirp is the projective chirp, of the form , having the three parameters a (scale), b (translation), and c (chirpiness). The projective chirp is ideally suited to image processing In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as photographs or frames of video; the output of image processing can be either an image or a set of characteristics or parameters related to the image. Most image-processing techniques involve treating the image, and forms the basis for the projective chirplet transform In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets.

Key chirp

A change in frequency of Morse code Morse code is a type of character encoding that transmits telegraphic information using rhythm. Morse code uses a standardized sequence of short and long elements to represent the letters, numerals, punctuation and special characters of a given message. The short and long elements can be formed by sounds, marks, or pulses, in on off keying and are from the desired frequency, due to poor stability in the RF Oscillator Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation.& is known as chirp^[1], and in the RST code The RST code is used by amateur radio operators, shortwave listeners, and other radio hobbyists to exchange information about the quality of a radio signal being received. The code is a three digit number, with one digit each for conveying an assessment of the signal's readability, strength, and tone. The code was developed in the early 20th is given an appended letter 'C'.

See also

• Chirplet transform In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets — 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 Pulse compression is a signal processing technique mainly used in radar, sonar and echography to augment the range resolution as well as the signal to noise ratio. This is achieved by modulating the transmitted pulse and then correlating the received signal with the transmitted pulse - 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 Chirp spread spectrum is a spread spectrum technique that uses wideband linear frequency modulated chirp pulses to encode information. A chirp is a sinusoidal signal whose frequency increases or decreases over a certain amount of time. Below is an example of an upchirp - as you can see, the frequency increases linearly over time - A part of the wireless telecommunications standard IEEE 802.15.4a CSS (see Chirp Spread Spectrum (CSS) PHY Presentation for IEEE P802.15.4a).
• continuous-wave radar Continuous-wave radar system is a radar system where a known stable frequency continuous wave radio energy is transmitted and then received from any reflecting objects. The return frequencies are shifted away from the transmitted frequency based on the Doppler effect if they are moving
• SHARAD SHARAD is a subsurface sounding radar embarked on the Mars Reconnaissance Orbiter probe. It complements the MARSIS instrument on Mars Express, providing lower penetration capabilities (some hundred meters) but much finer resolution (15 metres - untapered - in free space)
• chirped pulse amplification Chirped pulse amplification or optical parametric chirped pulse amplification (OPCPA), is a technique for amplifying an ultrashort laser pulse up to the petawatt level with the laser pulse being stretched out temporally and spectrally prior to amplification. CPA is the current state of the art technique which all of the highest power lasers (
• chirped mirror A chirped mirror is a dielectric mirror with chirped spaces—spaces of varying depth designed to reflect varying wavelengths of lights—between the dielectric layers
• dispersion (optics) In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency. Media having such a property are termed dispersive media. Dispersion is sometimes called chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity

References

1. ^ The Beginner's Handbook of Amateur Radio By Clay Laster

Categories: Signal processing Categories: Electrical engineering | Communication engineering | Fields of application of statistics

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