A chirp is a
signal in which the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
increases (''up-chirp'') or decreases (''down-chirp'') with time. In some sources, the term ''chirp'' is used interchangeably with sweep signal. It is commonly applied to
sonar
Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances (ranging), communicate with or detect objects on o ...
,
radar
Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor v ...
, and
laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The ...
systems, and to other applications, such as in
spread-spectrum
In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g., an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency do ...
communications (see
chirp spread spectrum). This signal type is biologically inspired and occurs as a phenomenon due to dispersion (a non-linear dependence between frequency and the propagation speed of the wave components). It is usually compensated for by using a matched filter, which can be part of the propagation channel. Depending on the specific performance measure, however, there are better techniques both for radar and communication. Since it was used in radar and space, it has been adopted also for communication standards. For automotive radar applications, it is usually called linear frequency modulated waveform (LFMW).
In spread-spectrum usage,
surface acoustic wave (SAW) devices are often used to generate and demodulate the chirped signals. In
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
,
ultrashort laser
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The ...
pulses also exhibit chirp, which, in optical transmission systems, interacts with the
dispersion
Dispersion may refer to:
Economics and finance
*Dispersion (finance), a measure for the statistical distribution of portfolio returns
*Price dispersion, a variation in prices across sellers of the same item
*Wage dispersion, the amount of variatio ...
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
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
is defined as:
:
then the
instantaneous angular frequency
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''comple ...
, ''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.
[
]
Types
Linear
In a linear-frequency chirp or simply linear chirp, the instantaneous frequency varies exactly linearly with time:
:,
where is the starting frequency (at time ) and is the chirp rate, assumed constant:
:.
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.
The corresponding time-domain function for a sinusoidal
A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often i ...
linear chirp is the sine of the phase in radians:
: