<s>
A	O
heterodyne	B-Algorithm
is	O
a	O
signal	O
frequency	O
that	O
is	O
created	O
by	O
combining	O
or	O
mixing	O
two	O
other	O
frequencies	O
using	O
a	O
signal	O
processing	O
technique	O
called	O
heterodyning	B-Algorithm
,	O
which	O
was	O
invented	O
by	O
Canadian	O
inventor-engineer	O
Reginald	O
Fessenden	O
.	O
</s>
<s>
Heterodyning	B-Algorithm
is	O
used	O
to	O
shift	O
signals	O
from	O
one	O
frequency	O
range	O
into	O
another	O
,	O
and	O
is	O
also	O
involved	O
in	O
the	O
processes	O
of	O
modulation	B-Application
and	O
demodulation	B-Device
.	O
</s>
<s>
The	O
two	O
input	O
frequencies	O
are	O
combined	O
in	O
a	O
nonlinear	O
signal-processing	O
device	O
such	O
as	O
a	O
vacuum	O
tube	O
,	O
transistor	B-Application
,	O
or	O
diode	O
,	O
usually	O
called	O
a	O
mixer	O
.	O
</s>
<s>
The	O
new	O
signal	O
frequencies	O
are	O
called	O
heterodynes	B-Algorithm
.	O
</s>
<s>
Typically	O
,	O
only	O
one	O
of	O
the	O
heterodynes	B-Algorithm
is	O
required	O
and	O
the	O
other	O
signal	O
is	O
filtered	O
out	O
of	O
the	O
output	O
of	O
the	O
mixer	O
.	O
</s>
<s>
Heterodyne	B-Algorithm
frequencies	O
are	O
related	O
to	O
the	O
phenomenon	O
of	O
"	O
beats	O
"	O
in	O
acoustics	O
.	O
</s>
<s>
A	O
major	O
application	O
of	O
the	O
heterodyne	B-Algorithm
process	O
is	O
in	O
the	O
superheterodyne	O
radio	O
receiver	O
circuit	O
,	O
which	O
is	O
used	O
in	O
virtually	O
all	O
modern	O
radio	O
receivers	O
.	O
</s>
<s>
In	O
1901	O
,	O
Reginald	O
Fessenden	O
demonstrated	O
a	O
direct-conversion	O
heterodyne	B-Algorithm
receiver	O
or	O
beat	B-Application
receiver	O
as	O
a	O
method	O
of	O
making	O
continuous	O
wave	O
radiotelegraphy	O
signals	O
audible	O
.	O
</s>
<s>
This	O
ringing	O
would	O
quickly	O
decay	O
,	O
so	O
the	O
output	O
of	O
the	O
transmitter	O
would	O
be	O
a	O
succession	O
of	O
damped	B-Device
waves	I-Device
.	O
</s>
<s>
When	O
these	O
damped	B-Device
waves	I-Device
were	O
received	O
by	O
a	O
simple	O
detector	B-Algorithm
,	O
the	O
operator	O
would	O
hear	O
an	O
audible	O
buzzing	O
sound	O
that	O
could	O
be	O
transcribed	O
back	O
into	O
alpha-numeric	O
characters	O
.	O
</s>
<s>
With	O
the	O
development	O
of	O
the	O
arc	O
converter	O
radio	O
transmitter	O
in	O
1904	O
,	O
continuous	O
wave	O
(	O
CW	O
)	O
modulation	B-Application
began	O
to	O
be	O
used	O
for	O
radiotelegraphy	O
.	O
</s>
<s>
CW	O
Morse	O
code	O
signals	O
are	O
not	O
amplitude	O
modulated	B-Application
,	O
but	O
rather	O
consist	O
of	O
bursts	O
of	O
sinusoidal	O
carrier	O
frequency	O
.	O
</s>
<s>
The	O
direct-conversion	O
(	O
heterodyne	B-Algorithm
)	O
detector	B-Algorithm
was	O
invented	O
to	O
make	O
continuous	O
wave	O
radio-frequency	O
signals	O
audible	O
.	O
</s>
<s>
The	O
"	O
heterodyne	B-Algorithm
"	O
or	O
"	O
beat	B-Application
"	O
receiver	O
has	O
a	O
local	O
oscillator	O
that	O
produces	O
a	O
radio	O
signal	O
adjusted	O
to	O
be	O
close	O
in	O
frequency	O
to	O
the	O
incoming	O
signal	O
being	O
received	O
.	O
</s>
<s>
When	O
the	O
two	O
signals	O
are	O
mixed	O
,	O
a	O
"	O
beat	B-Application
"	O
frequency	O
equal	O
to	O
the	O
difference	O
between	O
the	O
two	O
frequencies	O
is	O
created	O
.	O
</s>
<s>
Adjusting	O
the	O
local	O
oscillator	O
frequency	O
correctly	O
puts	O
the	O
beat	B-Application
frequency	I-Application
in	O
the	O
audio	O
range	O
,	O
where	O
it	O
can	O
be	O
heard	O
as	O
a	O
tone	O
in	O
the	O
receiver	O
's	O
earphones	O
whenever	O
the	O
transmitter	O
signal	O
is	O
present	O
.	O
</s>
<s>
This	O
technique	O
is	O
still	O
used	O
in	O
radio	O
telegraphy	O
,	O
the	O
local	O
oscillator	O
now	O
being	O
called	O
the	O
beat	B-Application
frequency	I-Application
oscillator	O
or	O
BFO	O
.	O
</s>
<s>
Fessenden	O
coined	O
the	O
word	O
heterodyne	B-Algorithm
from	O
the	O
Greek	O
roots	O
hetero	O
-	O
"	O
different	O
"	O
,	O
and	O
dyn	O
-	O
"	O
power	O
"	O
(	O
cf	O
.	O
</s>
<s>
An	O
important	O
and	O
widely	O
used	O
application	O
of	O
the	O
heterodyne	B-Algorithm
technique	O
is	O
in	O
the	O
superheterodyne	O
receiver	O
(	O
superhet	O
)	O
,	O
which	O
was	O
invented	O
by	O
U.S.	O
engineer	O
Edwin	O
Howard	O
Armstrong	O
in	O
1918	O
.	O
</s>
<s>
The	O
IF	O
signal	O
is	O
amplified	O
and	O
filtered	O
and	O
then	O
applied	O
to	O
a	O
detector	B-Algorithm
that	O
extracts	O
the	O
audio	O
signal	O
;	O
the	O
audio	O
is	O
ultimately	O
sent	O
to	O
the	O
receiver	O
's	O
loudspeaker	O
.	O
</s>
<s>
To	O
first	O
order	O
,	O
an	O
amplifying	O
device	O
has	O
a	O
fixed	O
gain-bandwidth	O
product	O
.	O
</s>
<s>
If	O
the	O
device	O
has	O
a	O
gain-bandwidth	O
product	O
of	O
60MHz	O
,	O
then	O
it	O
can	O
provide	O
a	O
voltage	O
gain	O
of	O
3	O
at	O
an	O
RF	O
of	O
20MHz	O
or	O
a	O
voltage	O
gain	O
of	O
30	O
at	O
an	O
IF	O
of	O
2MHz	O
.	O
</s>
<s>
Heterodyning	B-Algorithm
,	O
also	O
called	O
frequency	O
conversion	O
,	O
is	O
used	O
very	O
widely	O
in	O
communications	O
engineering	O
to	O
generate	O
new	O
frequencies	O
and	O
move	O
information	O
from	O
one	O
frequency	O
channel	O
to	O
another	O
.	O
</s>
<s>
Besides	O
its	O
use	O
in	O
the	O
superheterodyne	O
circuit	O
found	O
in	O
almost	O
all	O
radio	O
and	O
television	O
receivers	O
,	O
it	O
is	O
used	O
in	O
radio	O
transmitters	O
,	O
modems	B-Application
,	O
satellite	B-Application
communications	O
and	O
set-top	O
boxes	O
,	O
radar	B-Application
,	O
radio	O
telescopes	O
,	O
telemetry	O
systems	O
,	O
cell	O
phones	O
,	O
cable	O
television	O
converter	O
boxes	O
and	O
headends	O
,	O
microwave	B-Application
relays	I-Application
,	O
metal	O
detectors	B-Algorithm
,	O
atomic	O
clocks	O
,	O
and	O
military	O
electronic	O
countermeasure	O
(	O
jamming	O
)	O
systems	O
.	O
</s>
<s>
In	O
large	O
scale	O
telecommunication	O
networks	O
such	O
as	O
telephone	O
network	O
trunks	O
,	O
microwave	B-Application
relay	I-Application
networks	O
,	O
cable	O
television	O
systems	O
,	O
and	O
communication	O
satellite	B-Application
links	O
,	O
large	O
bandwidth	B-Algorithm
capacity	O
links	O
are	O
shared	O
by	O
many	O
individual	O
communication	O
channels	O
by	O
using	O
heterodyning	B-Algorithm
to	O
move	O
the	O
frequency	O
of	O
the	O
individual	O
signals	O
up	O
to	O
different	O
frequencies	O
,	O
which	O
share	O
the	O
channel	O
.	O
</s>
<s>
This	O
is	O
called	O
frequency	B-Protocol
division	I-Protocol
multiplexing	I-Protocol
(	O
FDM	O
)	O
.	O
</s>
<s>
They	O
do	O
this	O
by	O
mixing	O
the	O
television	O
signal	O
frequency	O
,	O
fCH	O
with	O
a	O
local	O
oscillator	O
at	O
a	O
much	O
higher	O
frequency	O
,	O
creating	O
a	O
heterodyne	B-Algorithm
at	O
the	O
sum	O
,	O
which	O
is	O
added	O
to	O
the	O
cable	O
.	O
</s>
<s>
At	O
the	O
consumer	O
's	O
home	O
,	O
the	O
cable	O
set	O
top	O
box	O
has	O
a	O
downconverter	B-Algorithm
that	O
mixes	O
the	O
incoming	O
signal	O
at	O
frequency	O
with	O
the	O
same	O
local	O
oscillator	O
frequency	O
creating	O
the	O
difference	O
heterodyne	B-Algorithm
frequency	O
,	O
converting	O
the	O
television	O
channel	O
back	O
to	O
its	O
original	O
frequency	O
:	O
.	O
</s>
<s>
The	O
original	O
lower	O
basic	O
frequency	O
of	O
the	O
signal	O
is	O
called	O
the	O
baseband	B-Algorithm
,	O
while	O
the	O
higher	O
channel	O
it	O
is	O
moved	O
to	O
is	O
called	O
the	O
passband	B-Algorithm
.	O
</s>
<s>
Many	O
analog	O
videotape	O
systems	O
rely	O
on	O
a	O
downconverted	O
color	O
subcarrier	O
to	O
record	O
color	O
information	O
in	O
their	O
limited	O
bandwidth	B-Algorithm
.	O
</s>
<s>
These	O
systems	O
are	O
referred	O
to	O
as	O
"	O
heterodyne	B-Algorithm
systems	O
"	O
or	O
"	O
color-under	O
systems	O
"	O
.	O
</s>
<s>
PAL	B-Language
VHS	O
color	O
subcarrier	O
is	O
similarly	O
downconverted	O
(	O
but	O
from	O
4.43MHz	O
)	O
.	O
</s>
<s>
The	O
now-obsolete	O
3/4	O
"	O
U-matic	O
systems	O
use	O
a	O
heterodyned	O
~	O
688kHz	O
subcarrier	O
for	O
NTSC	O
recordings	O
(	O
as	O
does	O
Sony	O
's	O
Betamax	O
,	O
which	O
is	O
at	O
its	O
basis	O
a	O
1/2	O
″	O
consumer	O
version	O
of	O
U-matic	O
)	O
,	O
while	O
PAL	B-Language
U-matic	O
decks	O
came	O
in	O
two	O
mutually	O
incompatible	O
varieties	O
,	O
with	O
different	O
subcarrier	O
frequencies	O
,	O
known	O
as	O
Hi-Band	O
and	O
Low-Band	O
.	O
</s>
<s>
Other	O
videotape	O
formats	O
with	O
heterodyne	B-Algorithm
color	O
systems	O
include	O
Video-8	O
and	O
Hi8	O
.	O
</s>
<s>
The	O
heterodyne	B-Algorithm
system	O
in	O
these	O
cases	O
is	O
used	O
to	O
convert	O
quadrature	O
phase-encoded	O
and	O
amplitude	O
modulated	B-Application
sine	O
waves	O
from	O
the	O
broadcast	O
frequencies	O
to	O
frequencies	O
recordable	O
in	O
less	O
than	O
1MHz	O
bandwidth	B-Algorithm
.	O
</s>
<s>
The	O
theremin	O
,	O
an	O
electronic	O
musical	O
instrument	O
,	O
traditionally	O
uses	O
the	O
heterodyne	B-Algorithm
principle	I-Algorithm
to	O
produce	O
a	O
variable	O
audio	O
frequency	O
in	O
response	O
to	O
the	O
movement	O
of	O
the	O
musician	O
's	O
hands	O
in	O
the	O
vicinity	O
of	O
one	O
or	O
more	O
antennae	O
,	O
which	O
act	O
as	O
capacitor	O
plates	O
.	O
</s>
<s>
The	O
ring	O
modulator	B-Application
is	O
a	O
type	O
of	O
frequency	O
mixer	O
incorporated	O
into	O
some	O
synthesizers	O
or	O
used	O
as	O
a	O
stand-alone	O
audio	O
effect	O
.	O
</s>
<s>
Optical	O
heterodyne	B-Algorithm
detection	I-Algorithm
(	O
an	O
area	O
of	O
active	O
research	O
)	O
is	O
an	O
extension	O
of	O
the	O
heterodyning	B-Algorithm
technique	O
to	O
higher	O
(	O
visible	O
)	O
frequencies	O
.	O
</s>
<s>
Guerra	O
(	O
1995	O
)	O
first	O
published	O
the	O
results	O
of	O
what	O
he	O
called	O
a	O
"	O
form	O
of	O
optical	O
heterodyning	B-Algorithm
"	O
in	O
which	O
light	O
patterned	O
by	O
a	O
50	O
nm	O
pitch	O
grating	O
illuminated	O
a	O
second	O
grating	O
of	O
pitch	O
50	O
nm	O
,	O
with	O
the	O
gratings	O
rotated	O
with	O
respect	O
to	O
each	O
other	O
by	O
the	O
angular	O
amount	O
needed	O
to	O
achieve	O
magnification	O
.	O
</s>
<s>
This	O
super-resolution	O
microscopic	O
imaging	O
through	O
optical	O
heterodyning	B-Algorithm
later	O
came	O
to	O
be	O
know	O
by	O
many	O
as	O
"	O
structured	O
illumination	O
microscopy	O
"	O
.	O
</s>
<s>
In	O
addition	O
to	O
super-resolution	O
optical	O
microscopy	O
,	O
optical	O
heterodyning	B-Algorithm
could	O
greatly	O
improve	O
optical	O
modulators	B-Application
,	O
increasing	O
the	O
density	O
of	O
information	O
carried	O
by	O
optical	B-Architecture
fibers	I-Architecture
.	O
</s>
<s>
Since	O
optical	O
frequencies	O
are	O
far	O
beyond	O
the	O
manipulation	O
capacity	O
of	O
any	O
feasible	O
electronic	O
circuit	O
,	O
all	O
visible	O
frequency	O
photon	O
detectors	B-Algorithm
are	O
inherently	O
energy	O
detectors	B-Algorithm
not	O
oscillating	O
electric	O
field	O
detectors	B-Algorithm
.	O
</s>
<s>
However	O
,	O
since	O
energy	O
detection	O
is	O
inherently	O
"	O
square-law	B-Algorithm
"	O
detection	O
,	O
it	O
intrinsically	O
mixes	O
any	O
optical	O
frequencies	O
present	O
on	O
the	O
detector	B-Algorithm
.	O
</s>
<s>
Thus	O
,	O
sensitive	O
detection	O
of	O
specific	O
optical	O
frequencies	O
necessitates	O
optical	O
heterodyne	B-Algorithm
detection	I-Algorithm
,	O
in	O
which	O
two	O
different	O
(	O
close-by	O
)	O
wavelengths	O
of	O
light	O
illuminate	O
the	O
detector	B-Algorithm
so	O
that	O
the	O
oscillating	O
electrical	O
output	O
corresponds	O
to	O
the	O
difference	O
between	O
their	O
frequencies	O
.	O
</s>
<s>
In	O
optical	O
Kerr	O
effect	O
(	O
OKE	O
)	O
spectroscopy	O
,	O
optical	O
heterodyning	B-Algorithm
of	O
the	O
OKE	O
signal	O
and	O
a	O
small	O
part	O
of	O
the	O
probe	O
signal	O
produces	O
a	O
mixed	O
signal	O
consisting	O
of	O
probe	O
,	O
heterodyne	B-Algorithm
OKE-probe	O
and	O
homodyne	O
OKE	O
signal	O
.	O
</s>
<s>
The	O
probe	O
and	O
homodyne	O
OKE	O
signals	O
can	O
be	O
filtered	O
out	O
,	O
leaving	O
the	O
heterodyne	B-Algorithm
frequency	O
signal	O
for	O
detection	O
.	O
</s>
<s>
Heterodyne	B-Algorithm
detection	I-Algorithm
is	O
often	O
used	O
in	O
interferometry	O
but	O
usually	O
confined	O
to	O
single	O
point	O
detection	O
rather	O
than	O
widefield	O
interferometry	O
,	O
however	O
,	O
widefield	O
heterodyne	B-Algorithm
interferometry	O
is	O
possible	O
using	O
a	O
special	O
camera	O
.	O
</s>
<s>
Heterodyning	B-Algorithm
is	O
based	O
on	O
the	O
trigonometric	O
identity	O
:	O
</s>
<s>
However	O
,	O
any	O
nonlinear	O
electronic	O
component	O
also	O
multiplies	O
signals	O
applied	O
to	O
it	O
,	O
producing	O
heterodyne	B-Algorithm
frequencies	O
in	O
its	O
output	O
—	O
so	O
a	O
variety	O
of	O
nonlinear	O
components	O
serve	O
as	O
mixers	O
.	O
</s>
<s>
Examples	O
of	O
nonlinear	O
components	O
that	O
are	O
used	O
as	O
mixers	O
are	O
vacuum	O
tubes	O
and	O
transistors	B-Application
biased	O
near	O
cutoff	O
(	O
class	O
C	O
)	O
,	O
and	O
diodes	O
.	O
</s>
<s>
In	O
nonlinear	O
optics	O
,	O
crystals	O
that	O
have	O
nonlinear	O
characteristics	O
are	O
used	O
to	O
mix	O
laser	O
light	O
beams	O
to	O
create	O
optical	O
heterodyne	B-Algorithm
frequencies	O
.	O
</s>
<s>
To	O
demonstrate	O
mathematically	O
how	O
a	O
nonlinear	O
component	O
can	O
multiply	O
signals	O
and	O
generate	O
heterodyne	B-Algorithm
frequencies	O
,	O
the	O
nonlinear	O
function	O
can	O
be	O
expanded	O
in	O
a	O
power	O
series	O
(	O
MacLaurin	O
series	O
)	O
:	O
</s>
<s>
These	O
unwanted	O
frequencies	O
,	O
along	O
with	O
the	O
unwanted	O
heterodyne	B-Algorithm
frequency	O
,	O
must	O
be	O
filtered	O
out	O
of	O
the	O
mixer	O
output	O
by	O
an	O
electronic	B-Architecture
filter	I-Architecture
to	O
leave	O
the	O
desired	O
frequency	O
.	O
</s>
