<s>
Bandwidth	B-Algorithm
is	O
the	O
difference	O
between	O
the	O
upper	O
and	O
lower	O
frequencies	O
in	O
a	O
continuous	O
band	B-Algorithm
of	I-Algorithm
frequencies	I-Algorithm
.	O
</s>
<s>
It	O
is	O
typically	O
measured	O
in	O
hertz	O
,	O
and	O
depending	O
on	O
context	O
,	O
may	O
specifically	O
refer	O
to	O
passband	B-Algorithm
bandwidth	B-Algorithm
or	O
baseband	B-Algorithm
bandwidth	B-Algorithm
.	O
</s>
<s>
Passband	B-Algorithm
bandwidth	B-Algorithm
is	O
the	O
difference	O
between	O
the	O
upper	O
and	O
lower	O
cutoff	O
frequencies	O
of	O
,	O
for	O
example	O
,	O
a	O
band-pass	O
filter	B-Architecture
,	O
a	O
communication	O
channel	O
,	O
or	O
a	O
signal	O
spectrum	O
.	O
</s>
<s>
Baseband	B-Algorithm
bandwidth	B-Algorithm
applies	O
to	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
or	O
baseband	B-Algorithm
signal	I-Algorithm
;	O
the	O
bandwidth	B-Algorithm
is	O
equal	O
to	O
its	O
upper	O
cutoff	O
frequency	O
.	O
</s>
<s>
Bandwidth	B-Algorithm
in	O
hertz	O
is	O
a	O
central	O
concept	O
in	O
many	O
fields	O
,	O
including	O
electronics	O
,	O
information	O
theory	O
,	O
digital	O
communications	O
,	O
radio	O
communications	O
,	O
signal	O
processing	O
,	O
and	O
spectroscopy	O
and	O
is	O
one	O
of	O
the	O
determinants	O
of	O
the	O
capacity	O
of	O
a	O
given	O
communication	O
channel	O
.	O
</s>
<s>
A	O
key	O
characteristic	O
of	O
bandwidth	B-Algorithm
is	O
that	O
any	O
band	O
of	O
a	O
given	O
width	O
can	O
carry	O
the	O
same	O
amount	O
of	O
information	O
,	O
regardless	O
of	O
where	O
that	O
band	O
is	O
located	O
in	O
the	O
frequency	O
spectrum	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
3kHz	O
band	O
can	O
carry	O
a	O
telephone	O
conversation	O
whether	O
that	O
band	O
is	O
at	O
baseband	B-Algorithm
(	O
as	O
in	O
a	O
POTS	O
telephone	O
line	O
)	O
or	O
modulated	B-Application
to	O
some	O
higher	O
frequency	O
.	O
</s>
<s>
However	O
,	O
wide	O
bandwidths	B-Algorithm
are	O
easier	O
to	O
obtain	O
and	O
process	O
at	O
higher	O
frequencies	O
because	O
the	O
is	O
smaller	O
.	O
</s>
<s>
Bandwidth	B-Algorithm
is	O
a	O
key	O
concept	O
in	O
many	O
telecommunications	O
applications	O
.	O
</s>
<s>
In	O
radio	O
communications	O
,	O
for	O
example	O
,	O
bandwidth	B-Algorithm
is	O
the	O
frequency	O
range	O
occupied	O
by	O
a	O
modulated	B-Application
carrier	O
signal	O
.	O
</s>
<s>
An	O
FM	O
radio	O
receiver	B-Device
's	O
tuner	B-Device
spans	O
a	O
limited	O
range	O
of	O
frequencies	O
.	O
</s>
<s>
A	O
government	O
agency	O
(	O
such	O
as	O
the	O
Federal	O
Communications	O
Commission	O
in	O
the	O
United	O
States	O
)	O
may	O
apportion	O
the	O
regionally	O
available	O
bandwidth	B-Algorithm
to	O
broadcast	O
license	O
holders	O
so	O
that	O
their	O
signals	O
do	O
not	O
mutually	O
interfere	O
.	O
</s>
<s>
In	O
this	O
context	O
,	O
bandwidth	B-Algorithm
is	O
also	O
known	O
as	O
channel	O
spacing	O
.	O
</s>
<s>
One	O
definition	O
of	O
bandwidth	B-Algorithm
,	O
for	O
a	O
system	O
,	O
could	O
be	O
the	O
range	O
of	O
frequencies	O
over	O
which	O
the	O
system	O
produces	O
a	O
specified	O
level	O
of	O
performance	O
.	O
</s>
<s>
In	O
the	O
context	O
of	O
,	O
for	O
example	O
,	O
the	O
sampling	O
theorem	O
and	O
Nyquist	O
sampling	O
rate	O
,	O
bandwidth	B-Algorithm
typically	O
refers	O
to	O
baseband	B-Algorithm
bandwidth	B-Algorithm
.	O
</s>
<s>
In	O
the	O
context	O
of	O
Nyquist	O
symbol	O
rate	O
or	O
Shannon-Hartley	O
channel	O
capacity	O
for	O
communication	O
systems	O
it	O
refers	O
to	O
passband	B-Algorithm
bandwidth	B-Algorithm
.	O
</s>
<s>
For	O
example	O
,	O
a	O
one-microsecond	O
pulse	O
has	O
a	O
Rayleigh	O
bandwidth	B-Algorithm
of	O
one	O
megahertz	O
.	O
</s>
<s>
In	O
some	O
contexts	O
,	O
the	O
signal	B-Algorithm
bandwidth	I-Algorithm
in	O
hertz	O
refers	O
to	O
the	O
frequency	O
range	O
in	O
which	O
the	O
signal	O
's	O
spectral	B-Algorithm
density	I-Algorithm
(	O
in	O
W/Hz	B-Algorithm
or	O
V2/Hz	O
)	O
is	O
nonzero	O
or	O
above	O
a	O
small	O
threshold	O
value	O
.	O
</s>
<s>
The	O
threshold	O
value	O
is	O
often	O
defined	O
relative	O
to	O
the	O
maximum	O
value	O
,	O
and	O
is	O
most	O
commonly	O
the	O
,	O
that	O
is	O
the	O
point	O
where	O
the	O
spectral	B-Algorithm
density	I-Algorithm
is	O
half	O
its	O
maximum	O
value	O
(	O
or	O
the	O
spectral	O
amplitude	O
,	O
in	O
or	O
,	O
is	O
70.7	O
%	O
of	O
its	O
maximum	O
)	O
.	O
</s>
<s>
The	O
bandwidth	B-Algorithm
is	O
also	O
used	O
to	O
denote	O
system	O
bandwidth	B-Algorithm
,	O
for	O
example	O
in	O
filter	B-Architecture
or	O
communication	O
channel	O
systems	O
.	O
</s>
<s>
To	O
say	O
that	O
a	O
system	O
has	O
a	O
certain	O
bandwidth	B-Algorithm
means	O
that	O
the	O
system	O
can	O
process	O
signals	O
with	O
that	O
range	O
of	O
frequencies	O
,	O
or	O
that	O
the	O
system	O
reduces	O
the	O
bandwidth	B-Algorithm
of	O
a	O
white	O
noise	O
input	O
to	O
that	O
bandwidth	B-Algorithm
.	O
</s>
<s>
The	O
3dB	O
bandwidth	B-Algorithm
of	O
an	O
electronic	B-Architecture
filter	I-Architecture
or	O
communication	O
channel	O
is	O
the	O
part	O
of	O
the	O
system	O
's	O
frequency	O
response	O
that	O
lies	O
within	O
3dB	O
of	O
the	O
response	O
at	O
its	O
peak	O
,	O
which	O
,	O
in	O
the	O
passband	B-Algorithm
filter	B-Architecture
case	O
,	O
is	O
typically	O
at	O
or	O
near	O
its	O
center	O
frequency	O
,	O
and	O
in	O
the	O
low-pass	B-Algorithm
filter	I-Algorithm
is	O
at	O
or	O
near	O
its	O
cutoff	O
frequency	O
.	O
</s>
<s>
If	O
the	O
maximum	O
gain	O
is	O
0dB	O
,	O
the	O
3dB	O
bandwidth	B-Algorithm
is	O
the	O
frequency	O
range	O
where	O
attenuation	O
is	O
less	O
than	O
3dB	O
.	O
</s>
<s>
In	O
electronic	B-Architecture
filter	I-Architecture
design	O
,	O
a	O
filter	B-Architecture
specification	O
may	O
require	O
that	O
within	O
the	O
filter	B-Architecture
passband	B-Algorithm
,	O
the	O
gain	O
is	O
nominally	O
0dB	O
with	O
a	O
small	O
variation	O
,	O
for	O
example	O
within	O
the	O
±1dB	O
interval	O
.	O
</s>
<s>
In	O
a	O
transition	B-Algorithm
band	I-Algorithm
the	O
gain	O
is	O
not	O
specified	O
.	O
</s>
<s>
In	O
this	O
case	O
,	O
the	O
filter	B-Architecture
bandwidth	B-Algorithm
corresponds	O
to	O
the	O
passband	B-Algorithm
width	O
,	O
which	O
in	O
this	O
example	O
is	O
the	O
1dB-bandwidth	O
.	O
</s>
<s>
If	O
the	O
filter	B-Architecture
shows	O
amplitude	O
ripple	O
within	O
the	O
passband	B-Algorithm
,	O
the	O
xdB	O
point	O
refers	O
to	O
the	O
point	O
where	O
the	O
gain	O
is	O
xdB	O
below	O
the	O
nominal	O
passband	B-Algorithm
gain	O
rather	O
than	O
xdB	O
below	O
the	O
maximum	O
gain	O
.	O
</s>
<s>
In	O
signal	O
processing	O
and	O
control	O
theory	O
the	O
bandwidth	B-Algorithm
is	O
the	O
frequency	O
at	O
which	O
the	O
closed-loop	O
system	O
gain	O
drops	O
3dB	O
below	O
peak	O
.	O
</s>
<s>
In	O
communication	O
systems	O
,	O
in	O
calculations	O
of	O
the	O
Shannon	O
–	O
Hartley	O
channel	O
capacity	O
,	O
bandwidth	B-Algorithm
refers	O
to	O
the	O
3dB-bandwidth	O
.	O
</s>
<s>
In	O
calculations	O
of	O
the	O
maximum	O
symbol	O
rate	O
,	O
the	O
Nyquist	O
sampling	O
rate	O
,	O
and	O
maximum	O
bit	O
rate	O
according	O
to	O
the	O
Hartley	O
's	O
law	O
,	O
the	O
bandwidth	B-Algorithm
refers	O
to	O
the	O
frequency	O
range	O
within	O
which	O
the	O
gain	O
is	O
non-zero	O
.	O
</s>
<s>
The	O
fact	O
that	O
in	O
equivalent	B-Algorithm
baseband	I-Algorithm
models	I-Algorithm
of	O
communication	O
systems	O
,	O
the	O
signal	O
spectrum	O
consists	O
of	O
both	O
negative	O
and	O
positive	O
frequencies	O
,	O
can	O
lead	O
to	O
confusion	O
about	O
bandwidth	B-Algorithm
since	O
they	O
are	O
sometimes	O
referred	O
to	O
only	O
by	O
the	O
positive	O
half	O
,	O
and	O
one	O
will	O
occasionally	O
see	O
expressions	O
such	O
as	O
,	O
where	O
is	O
the	O
total	O
bandwidth	B-Algorithm
(	O
i.e.	O
</s>
<s>
the	O
maximum	O
passband	B-Algorithm
bandwidth	B-Algorithm
of	O
the	O
carrier-modulated	O
RF	O
signal	O
and	O
the	O
minimum	O
passband	B-Algorithm
bandwidth	B-Algorithm
of	O
the	O
physical	O
passband	B-Algorithm
channel	I-Algorithm
)	O
,	O
and	O
is	O
the	O
positive	O
bandwidth	B-Algorithm
(	O
the	O
baseband	B-Algorithm
bandwidth	B-Algorithm
of	O
the	O
equivalent	O
channel	O
model	O
)	O
.	O
</s>
<s>
For	O
instance	O
,	O
the	O
baseband	B-Algorithm
model	O
of	O
the	O
signal	O
would	O
require	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
with	O
cutoff	O
frequency	O
of	O
at	O
least	O
to	O
stay	O
intact	O
,	O
and	O
the	O
physical	O
passband	B-Algorithm
channel	I-Algorithm
would	O
require	O
a	O
passband	B-Algorithm
filter	B-Architecture
of	O
at	O
least	O
to	O
stay	O
intact	O
.	O
</s>
<s>
The	O
absolute	O
bandwidth	B-Algorithm
is	O
not	O
always	O
the	O
most	O
appropriate	O
or	O
useful	O
measure	O
of	O
bandwidth	B-Algorithm
.	O
</s>
<s>
For	O
instance	O
,	O
in	O
the	O
field	O
of	O
antennas	O
the	O
difficulty	O
of	O
constructing	O
an	O
antenna	O
to	O
meet	O
a	O
specified	O
absolute	O
bandwidth	B-Algorithm
is	O
easier	O
at	O
a	O
higher	O
frequency	O
than	O
at	O
a	O
lower	O
frequency	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
bandwidth	B-Algorithm
is	O
often	O
quoted	O
relative	O
to	O
the	O
frequency	O
of	O
operation	O
which	O
gives	O
a	O
better	O
indication	O
of	O
the	O
structure	O
and	O
sophistication	O
needed	O
for	O
the	O
circuit	O
or	O
device	O
under	O
consideration	O
.	O
</s>
<s>
There	O
are	O
two	O
different	O
measures	O
of	O
relative	O
bandwidth	B-Algorithm
in	O
common	O
use	O
:	O
fractional	O
bandwidth	B-Algorithm
(	O
)	O
and	O
ratio	O
bandwidth	B-Algorithm
(	O
)	O
.	O
</s>
<s>
In	O
the	O
following	O
,	O
the	O
absolute	O
bandwidth	B-Algorithm
is	O
defined	O
as	O
follows	O
,	O
</s>
<s>
Fractional	O
bandwidth	B-Algorithm
is	O
defined	O
as	O
the	O
absolute	O
bandwidth	B-Algorithm
divided	O
by	O
the	O
center	O
frequency	O
(	O
)	O
,	O
</s>
<s>
It	O
more	O
properly	O
reflects	O
the	O
logarithmic	O
relationship	O
of	O
fractional	O
bandwidth	B-Algorithm
with	O
increasing	O
frequency	O
.	O
</s>
<s>
Fractional	O
bandwidth	B-Algorithm
is	O
sometimes	O
expressed	O
as	O
a	O
percentage	O
of	O
the	O
center	O
frequency	O
(	O
percent	O
bandwidth	B-Algorithm
,	O
)	O
,	O
</s>
<s>
Ratio	O
bandwidth	B-Algorithm
is	O
defined	O
as	O
the	O
ratio	O
of	O
the	O
upper	O
and	O
lower	O
limits	O
of	O
the	O
band	O
,	O
</s>
<s>
Ratio	O
bandwidth	B-Algorithm
may	O
be	O
notated	O
as	O
.	O
</s>
<s>
The	O
relationship	O
between	O
ratio	O
bandwidth	B-Algorithm
and	O
fractional	O
bandwidth	B-Algorithm
is	O
given	O
by	O
,	O
</s>
<s>
Percent	O
bandwidth	B-Algorithm
is	O
a	O
less	O
meaningful	O
measure	O
in	O
wideband	O
applications	O
.	O
</s>
<s>
A	O
percent	O
bandwidth	B-Algorithm
of	O
100%	O
corresponds	O
to	O
a	O
ratio	O
bandwidth	B-Algorithm
of	O
3:1	O
.	O
</s>
<s>
Ratio	O
bandwidth	B-Algorithm
is	O
often	O
expressed	O
in	O
octaves	B-Language
for	O
wideband	O
applications	O
.	O
</s>
<s>
An	O
octave	B-Language
is	O
a	O
frequency	O
ratio	O
of	O
2:1	O
leading	O
to	O
this	O
expression	O
for	O
the	O
number	O
of	O
octaves	B-Language
,	O
</s>
<s>
In	O
photonics	O
,	O
the	O
term	O
bandwidth	B-Algorithm
carries	O
a	O
variety	O
of	O
meanings	O
:	O
</s>
<s>
the	O
data	O
rate	O
(	O
e.g.	O
,	O
in	O
Gbit/s	O
)	O
achieved	O
in	O
an	O
optical	O
communication	O
system	O
;	O
see	O
bandwidth	B-Algorithm
(	O
computing	O
)	O
.	O
</s>
