# Dictionary Definition

chirrup n : a series of chirps [syn: twitter] v : make high-pitched
sounds; of birds [syn: peep, twirp, cheep, chirp]

# User Contributed Dictionary

## English

### Verb

to chirrup### Noun

- A series of chirps, clicks or clucks

### Quotations

- 1841 James Fenimore Cooper - The deerslayer: Or, the First
War-path
- When other folks' squirrels are at home and asleep, yourn keep in motion among the trees and chirrup and sing, in a way that even a Delaware gal can understand their music!

- 1859 Charled Dickens - The Cricket on the Hearth
- And here, if you like, the Cricket DID chime in ! with a Chirrup, Chirrup, Chirrup of such magnitude, by way of chorus

# Extensive Definition

A chirp is a
signal in which the frequency increases
('up-chirp') or decreases ('down-chirp') with time. It is commonly
used in sonar and radar, but has other applications,
such as in spread
spectrum communications. In spread spectrum usage, SAW
devices such as
RACs are often used to generate and demodulate the chirped
signals. In optics,
ultrashort
laser pulses also exhibit
chirp due to the dispersion of the materials
they propagate through.

In a linear chirp, the
instantaneous frequency f(t ) varies linearly with time:

- f(t) = f_0 + k t

where f0 is the starting frequency (at time t =
0), and k is the rate of frequency increase or chirp rate. A
corresponding time-domain function for a sinusoidal chirp is:

- x(t) = \sin(2 \pi \int_0^t f(t')\, dt') = \sin\left(2\pi (f_0 + \frac t) t \right)

In a geometric chirp, the frequency of the signal
varies with a geometric
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
as a function of time:

- f(t) = f_0 k^t

where f0 is the frequency at t=0, and k is the
rate of exponential
increase in frequency. A corresponding sinusoidal chirp
waveform would be defined by:

- x(t) = \sin(2 \pi f_0 \int_0^t k^ dt') = \sin\left(\frac ( k^t - 1)\right)

Although somewhat harder to generate, the
geometric type does not suffer from reduction in correlation gain if Doppler-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)_ = c f(t)_

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 via a
VCO, and a linearly or exponentially ramping control voltage. It can also be
generated digitally by a
DSP
and
DAC, perhaps by varying the phase angle coefficient in the
sinusoid generating function.

## 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
availablehttp://www.stanford.edu/~hengstle/References/Reference_5.pdf.

## Chirplet transform

Another kind of chirp is the projective chirp, of
the form g = f[(a \cdot x + b)/(c \cdot x + 1)], 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.

## 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 Chirp Spread Spectrum (CSS) PHY Presentation for IEEE P802.15.4a).

chirrup in German: Chirp

chirrup in French: Chirp

chirrup in Polish: Pulsed-FM