<s>
A	O
chirp	B-Algorithm
is	O
a	O
signal	O
in	O
which	O
the	O
frequency	O
increases	O
(	O
up-chirp	O
)	O
or	O
decreases	O
(	O
down-chirp	O
)	O
with	O
time	O
.	O
</s>
<s>
In	O
some	O
sources	O
,	O
the	O
term	O
chirp	B-Algorithm
is	O
used	O
interchangeably	O
with	O
sweep	O
signal	O
.	O
</s>
<s>
It	O
is	O
commonly	O
applied	O
to	O
sonar	B-Application
,	O
radar	B-Application
,	O
and	O
laser	O
systems	O
,	O
and	O
to	O
other	O
applications	O
,	O
such	O
as	O
in	O
spread-spectrum	B-Architecture
communications	O
(	O
see	O
chirp	B-Protocol
spread	I-Protocol
spectrum	I-Protocol
)	O
.	O
</s>
<s>
Depending	O
on	O
the	O
specific	O
performance	O
measure	O
,	O
however	O
,	O
there	O
are	O
better	O
techniques	O
both	O
for	O
radar	B-Application
and	O
communication	O
.	O
</s>
<s>
Since	O
it	O
was	O
used	O
in	O
radar	B-Application
and	O
space	O
,	O
it	O
has	O
been	O
adopted	O
also	O
for	O
communication	O
standards	O
.	O
</s>
<s>
For	O
automotive	O
radar	B-Application
applications	O
,	O
it	O
is	O
usually	O
called	O
linear	O
frequency	O
modulated	O
waveform	O
(	O
LFMW	O
)	O
.	O
</s>
<s>
In	O
spread-spectrum	B-Architecture
usage	O
,	O
surface	O
acoustic	O
wave	O
(	O
SAW	O
)	O
devices	O
are	O
often	O
used	O
to	O
generate	O
and	O
demodulate	O
the	O
chirped	O
signals	O
.	O
</s>
<s>
In	O
optics	B-Algorithm
,	O
ultrashort	O
laser	O
pulses	O
also	O
exhibit	O
chirp	B-Algorithm
,	O
which	O
,	O
in	O
optical	O
transmission	O
systems	O
,	O
interacts	O
with	O
the	O
dispersion	O
properties	O
of	O
the	O
materials	O
,	O
increasing	O
or	O
decreasing	O
total	O
pulse	O
dispersion	O
as	O
the	O
signal	O
propagates	O
.	O
</s>
<s>
In	O
a	O
linear-frequency	O
chirp	B-Algorithm
or	O
simply	O
linear	O
chirp	B-Algorithm
,	O
the	O
instantaneous	O
frequency	O
varies	O
exactly	O
linearly	O
with	O
time	O
:	O
</s>
<s>
where	O
is	O
the	O
starting	O
frequency	O
(	O
at	O
time	O
)	O
and	O
is	O
the	O
chirp	B-Algorithm
rate	O
,	O
assumed	O
constant	O
:	O
</s>
<s>
For	O
the	O
linear	O
chirp	B-Algorithm
,	O
this	O
results	O
in	O
:	O
</s>
<s>
The	O
corresponding	O
time-domain	O
function	O
for	O
a	O
sinusoidal	O
linear	O
chirp	B-Algorithm
is	O
the	O
sine	O
of	O
the	O
phase	O
in	O
radians	O
:	O
</s>
<s>
In	O
a	O
geometric	O
chirp	B-Algorithm
,	O
also	O
called	O
an	O
exponential	O
chirp	B-Algorithm
,	O
the	O
frequency	O
of	O
the	O
signal	O
varies	O
with	O
a	O
geometric	O
relationship	O
over	O
time	O
.	O
</s>
<s>
In	O
an	O
exponential	O
chirp	B-Algorithm
,	O
the	O
frequency	O
of	O
the	O
signal	O
varies	O
exponentially	O
as	O
a	O
function	O
of	O
time	O
:	O
</s>
<s>
Unlike	O
the	O
linear	O
chirp	B-Algorithm
,	O
which	O
has	O
a	O
constant	O
chirpyness	O
,	O
an	O
exponential	O
chirp	B-Algorithm
has	O
an	O
exponentially	O
increasing	O
frequency	O
rate	O
.	O
</s>
<s>
The	O
corresponding	O
time-domain	O
function	O
for	O
the	O
phase	O
of	O
an	O
exponential	O
chirp	B-Algorithm
is	O
the	O
integral	O
of	O
the	O
frequency	O
:	O
</s>
<s>
The	O
corresponding	O
time-domain	O
function	O
for	O
a	O
sinusoidal	O
exponential	O
chirp	B-Algorithm
is	O
the	O
sine	O
of	O
the	O
phase	O
in	O
radians	O
:	O
</s>
<s>
As	O
was	O
the	O
case	O
for	O
the	O
Linear	O
Chirp	B-Algorithm
,	O
the	O
instantaneous	O
frequency	O
of	O
the	O
Exponential	O
Chirp	B-Algorithm
consists	O
of	O
the	O
fundamental	O
frequency	O
accompanied	O
by	O
additional	O
harmonics	O
.	O
</s>
<s>
Hyperbolic	O
chirps	B-Algorithm
are	O
used	O
in	O
radar	B-Application
applications	O
,	O
as	O
they	O
show	O
maximum	O
matched	O
filter	O
response	O
after	O
being	O
distorted	O
by	O
the	O
Doppler	O
effect	O
.	O
</s>
<s>
In	O
a	O
hyperbolic	O
chirp	B-Algorithm
,	O
the	O
frequency	O
of	O
the	O
signal	O
varies	O
hyperbolically	O
as	O
a	O
function	O
of	O
time	O
:	O
</s>
<s>
The	O
corresponding	O
time-domain	O
function	O
for	O
the	O
phase	O
of	O
an	O
hyperbolic	O
chirp	B-Algorithm
is	O
the	O
integral	O
of	O
the	O
frequency	O
:	O
</s>
<s>
The	O
corresponding	O
time-domain	O
function	O
for	O
a	O
sinusoidal	O
hyperbolic	O
chirp	B-Algorithm
is	O
the	O
sine	O
of	O
the	O
phase	O
in	O
radians	O
:	O
</s>
<s>
A	O
chirp	B-Algorithm
signal	I-Algorithm
can	O
be	O
generated	O
with	O
analog	O
circuitry	O
via	O
a	O
voltage-controlled	O
oscillator	O
(	O
VCO	O
)	O
,	O
and	O
a	O
linearly	O
or	O
exponentially	O
ramping	O
control	O
voltage	O
.	O
</s>
<s>
It	O
can	O
also	O
be	O
generated	O
digitally	B-General_Concept
by	O
a	O
digital	B-Architecture
signal	I-Architecture
processor	I-Architecture
(	O
DSP	O
)	O
and	O
digital-to-analog	O
converter	O
(	O
DAC	O
)	O
,	O
using	O
a	O
direct	O
digital	O
synthesizer	O
(	O
DDS	O
)	O
and	O
by	O
varying	O
the	O
step	O
in	O
the	O
numerically	O
controlled	O
oscillator	O
.	O
</s>
<s>
It	O
can	O
also	O
be	O
generated	O
by	O
a	O
YIG	B-Algorithm
oscillator	I-Algorithm
.	O
</s>
<s>
A	O
chirp	B-Algorithm
signal	I-Algorithm
shares	O
the	O
same	O
spectral	O
content	O
with	O
an	O
impulse	O
signal	O
.	O
</s>
<s>
However	O
,	O
unlike	O
in	O
the	O
impulse	O
signal	O
,	O
spectral	O
components	O
of	O
the	O
chirp	B-Algorithm
signal	I-Algorithm
have	O
different	O
phases	O
,	O
i.e.	O
,	O
their	O
power	O
spectra	O
are	O
alike	O
but	O
the	O
phase	O
spectra	O
are	O
distinct	O
.	O
</s>
<s>
Dispersion	O
of	O
a	O
signal	O
propagation	O
medium	O
may	O
result	O
in	O
unintentional	O
conversion	O
of	O
impulse	O
signals	O
into	O
chirps	B-Algorithm
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
many	O
practical	O
applications	O
,	O
such	O
as	O
chirped	O
pulse	O
amplifiers	O
or	O
echolocation	O
systems	O
,	O
use	O
chirp	B-Algorithm
signals	I-Algorithm
instead	O
of	O
impulses	O
because	O
of	O
their	O
inherently	O
lower	O
peak-to-average	O
power	O
ratio	O
(	O
PAPR	O
)	O
.	O
</s>
<s>
Chirp	B-Algorithm
modulation	O
,	O
or	O
linear	O
frequency	O
modulation	O
for	O
digital	O
communication	O
,	O
was	O
patented	O
by	O
Sidney	O
Darlington	O
in	O
1954	O
with	O
significant	O
later	O
work	O
performed	O
by	O
Winkler	O
in	O
1962	O
.	O
</s>
<s>
These	O
waveforms	O
are	O
commonly	O
referred	O
to	O
as	O
linear	O
chirps	B-Algorithm
or	O
simply	O
chirps	B-Algorithm
.	O
</s>
<s>
Hence	O
the	O
rate	O
at	O
which	O
their	O
frequency	O
changes	O
is	O
called	O
the	O
chirp	B-Algorithm
rate	O
.	O
</s>
<s>
In	O
binary	O
chirp	B-Algorithm
modulation	O
,	O
binary	O
data	O
is	O
transmitted	O
by	O
mapping	O
the	O
bits	O
into	O
chirps	B-Algorithm
of	O
opposite	O
chirp	B-Algorithm
rates	O
.	O
</s>
<s>
For	O
instance	O
,	O
over	O
one	O
bit	O
period	O
"	O
1	O
"	O
is	O
assigned	O
a	O
chirp	B-Algorithm
with	O
positive	O
rate	O
a	O
and	O
"	O
0	O
"	O
a	O
chirp	B-Algorithm
with	O
negative	O
rate	O
−a	O
.	O
</s>
<s>
Chirps	B-Algorithm
have	O
been	O
heavily	O
used	O
in	O
radar	B-Application
applications	O
and	O
as	O
a	O
result	O
advanced	O
sources	O
for	O
transmission	O
and	O
matched	O
filters	O
for	O
reception	O
of	O
linear	O
chirps	B-Algorithm
are	O
available	O
.	O
</s>
<s>
Another	O
kind	O
of	O
chirp	B-Algorithm
is	O
the	O
projective	O
chirp	B-Algorithm
,	O
of	O
the	O
form	O
:	O
</s>
<s>
The	O
projective	O
chirp	B-Algorithm
is	O
ideally	O
suited	O
to	O
image	B-Algorithm
processing	I-Algorithm
,	O
and	O
forms	O
the	O
basis	O
for	O
the	O
projective	O
chirplet	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
A	O
change	O
in	O
frequency	O
of	O
Morse	O
code	O
from	O
the	O
desired	O
frequency	O
,	O
due	O
to	O
poor	O
stability	O
in	O
the	O
RF	O
oscillator	O
,	O
is	O
known	O
as	O
chirp	B-Algorithm
,	O
and	O
in	O
the	O
R-S-T	O
system	O
is	O
given	O
an	O
appended	O
letter	O
'	O
C	O
 '	O
.	O
</s>
