<s>
Angle	B-Device
modulation	I-Device
is	O
a	O
class	O
of	O
carrier	O
modulation	B-Application
that	O
is	O
used	O
in	O
telecommunications	O
transmission	O
systems	O
.	O
</s>
<s>
The	O
class	O
comprises	O
frequency	B-Application
modulation	I-Application
(	O
FM	B-Application
)	O
and	O
phase	B-Device
modulation	I-Device
(	O
PM	O
)	O
,	O
and	O
is	O
based	O
on	O
altering	O
the	O
frequency	O
or	O
the	O
phase	O
,	O
respectively	O
,	O
of	O
a	O
carrier	O
signal	O
to	O
encode	O
the	O
message	O
signal	O
.	O
</s>
<s>
This	O
contrasts	O
with	O
varying	O
the	O
amplitude	B-Application
of	O
the	O
carrier	O
,	O
practiced	O
in	O
amplitude	B-Device
modulation	I-Device
(	O
AM	O
)	O
transmission	O
,	O
the	O
earliest	O
of	O
the	O
major	O
modulation	B-Application
methods	O
used	O
widely	O
in	O
early	O
radio	O
broadcasting	O
.	O
</s>
<s>
In	O
general	O
form	O
,	O
an	O
analog	B-Application
modulation	I-Application
process	O
of	O
a	O
sinusoidal	O
carrier	O
wave	O
may	O
be	O
described	O
by	O
the	O
following	O
equation	O
:	O
</s>
<s>
A(t )	O
represents	O
the	O
time-varying	O
amplitude	B-Application
of	O
the	O
sinusoidal	O
carrier	O
wave	O
and	O
the	O
cosine-term	O
is	O
the	O
carrier	O
at	O
its	O
angular	O
frequency	O
,	O
and	O
the	O
instantaneous	O
phase	O
deviation	O
.	O
</s>
<s>
This	O
description	O
directly	O
provides	O
the	O
two	O
major	O
groups	O
of	O
modulation	B-Application
,	O
amplitude	B-Device
modulation	I-Device
and	O
angle	B-Device
modulation	I-Device
.	O
</s>
<s>
In	O
amplitude	B-Device
modulation	I-Device
,	O
the	O
angle	O
term	O
is	O
held	O
constant	O
,	O
while	O
in	O
angle	B-Device
modulation	I-Device
the	O
term	O
A(t )	O
is	O
constant	O
and	O
the	O
second	O
term	O
of	O
the	O
equation	O
has	O
a	O
functional	O
relationship	O
to	O
the	O
modulating	O
message	O
signal	O
.	O
</s>
<s>
The	O
functional	O
form	O
of	O
the	O
cosine	O
term	O
,	O
which	O
contains	O
the	O
expression	O
of	O
the	O
instantaneous	O
phase	O
as	O
its	O
argument	O
,	O
provides	O
the	O
distinction	O
of	O
the	O
two	O
types	O
of	O
angle	B-Device
modulation	I-Device
,	O
frequency	B-Application
modulation	I-Application
(	O
FM	B-Application
)	O
and	O
phase	B-Device
modulation	I-Device
(	O
PM	O
)	O
.	O
</s>
<s>
In	O
FM	B-Application
the	O
message	O
signal	O
causes	O
a	O
functional	O
variation	O
of	O
the	O
carrier	O
frequency	O
.	O
</s>
<s>
These	O
variations	O
are	O
controlled	O
by	O
both	O
the	O
frequency	O
and	O
the	O
amplitude	B-Application
of	O
the	O
modulating	O
wave	O
.	O
</s>
<s>
In	O
phase	B-Device
modulation	I-Device
,	O
the	O
instantaneous	O
phase	O
deviation	O
of	O
the	O
carrier	O
is	O
controlled	O
by	O
the	O
modulating	O
waveform	O
,	O
such	O
that	O
the	O
principal	O
frequency	O
remains	O
constant	O
.	O
</s>
<s>
For	O
frequency	B-Application
modulation	I-Application
,	O
the	O
instantaneous	O
frequency	O
of	O
an	O
angle-modulated	O
carrier	O
wave	O
is	O
given	O
by	O
the	O
first	O
derivative	O
with	O
respect	O
to	O
time	O
of	O
the	O
instantaneous	O
phase	O
:	O
</s>
<s>
In	O
principle	O
,	O
the	O
modulating	B-Application
signal	I-Application
in	O
both	O
frequency	O
and	O
phase	B-Device
modulation	I-Device
may	O
either	O
be	O
analog	O
in	O
nature	O
,	O
or	O
it	O
may	O
be	O
digital	O
.	O
</s>
<s>
In	O
general	O
,	O
however	O
,	O
when	O
using	O
digital	O
signals	O
to	O
modify	O
the	O
carrier	O
wave	O
,	O
the	O
method	O
is	O
called	O
keying	O
,	O
rather	O
than	O
modulation	B-Application
.	O
</s>
<s>
Thus	O
,	O
telecommunications	O
modems	B-Application
use	O
frequency-shift	O
keying	O
(	O
FSK	O
)	O
,	O
phase-shift	B-General_Concept
keying	I-General_Concept
(	O
PSK	O
)	O
,	O
or	O
amplitude-phase	B-Device
keying	I-Device
(	O
APK	O
)	O
,	O
or	O
various	O
combinations	O
.	O
</s>
<s>
Furthermore	O
,	O
another	O
digital	O
modulation	B-Application
is	O
line	B-Protocol
coding	I-Protocol
,	O
which	O
uses	O
a	O
baseband	B-Algorithm
carrier	O
,	O
rather	O
than	O
a	O
passband	B-Algorithm
wave	O
.	O
</s>
<s>
The	O
methods	O
of	O
angle	B-Device
modulation	I-Device
can	O
provide	O
better	O
discrimination	O
against	O
interference	O
and	O
noise	O
than	O
amplitude	B-Device
modulation	I-Device
.	O
</s>
<s>
Frequency	B-Application
modulation	I-Application
is	O
widely	O
used	O
for	O
FM	B-Application
broadcasting	O
of	O
radio	O
programming	O
,	O
and	O
largely	O
supplanted	O
amplitude	B-Device
modulation	I-Device
for	O
this	O
purpose	O
starting	O
in	O
the	O
1930s	O
,	O
with	O
its	O
invention	O
by	O
American	O
engineer	O
Edwin	O
Armstrong	O
in	O
1933	O
.	O
</s>
<s>
FM	B-Application
also	O
has	O
many	O
other	O
applications	O
,	O
such	O
as	O
in	O
two-way	O
radio	O
communications	O
,	O
and	O
in	O
FM	B-Application
synthesis	O
for	O
music	O
synthesizers	O
.	O
</s>
<s>
Phase	B-Device
modulation	I-Device
is	O
important	O
in	O
major	O
application	O
areas	O
including	O
cellular	O
and	O
satellite	O
telecommunications	O
,	O
as	O
well	O
as	O
in	O
data	O
networking	O
methods	O
,	O
such	O
as	O
in	O
some	O
digital	O
subscriber	O
line	O
systems	O
,	O
and	O
WiFi	O
.	O
</s>
<s>
The	O
combination	O
of	O
phase	B-Device
modulation	I-Device
with	O
amplitude	B-Device
modulation	I-Device
,	O
practiced	O
as	O
early	O
as	O
1874	O
by	O
Thomas	O
Edison	O
in	O
the	O
quadruplex	O
telegraph	O
for	O
transmitting	O
four	O
signals	O
,	O
two	O
each	O
in	O
both	O
directions	O
of	O
transmission	O
,	O
constitutes	O
the	O
polar	B-Protocol
modulation	I-Protocol
technique	O
.	O
</s>
