<s>
A	O
low-pass	B-Algorithm
filter	I-Algorithm
is	O
a	O
filter	O
that	O
passes	O
signals	O
with	O
a	O
frequency	O
lower	O
than	O
a	O
selected	O
cutoff	O
frequency	O
and	O
attenuates	O
signals	O
with	O
frequencies	O
higher	O
than	O
the	O
cutoff	O
frequency	O
.	O
</s>
<s>
The	O
filter	O
is	O
sometimes	O
called	O
a	O
high-cut	B-Algorithm
filter	I-Algorithm
,	O
or	O
treble-cut	B-Algorithm
filter	I-Algorithm
in	O
audio	O
applications	O
.	O
</s>
<s>
A	O
low-pass	B-Algorithm
filter	I-Algorithm
is	O
the	O
complement	O
of	O
a	O
high-pass	O
filter	O
.	O
</s>
<s>
In	O
optics	B-Algorithm
,	O
high-pass	O
and	O
low-pass	B-Algorithm
may	O
have	O
different	O
meanings	O
,	O
depending	O
on	O
whether	O
referring	O
to	O
frequency	O
or	O
wavelength	O
of	O
light	O
,	O
since	O
these	O
variables	O
are	O
inversely	O
related	O
.	O
</s>
<s>
High-pass	O
frequency	B-Architecture
filters	I-Architecture
would	O
act	O
as	O
low-pass	B-Algorithm
wavelength	O
filters	O
,	O
and	O
vice	O
versa	O
.	O
</s>
<s>
For	O
this	O
reason	O
it	O
is	O
a	O
good	O
practice	O
to	O
refer	O
to	O
wavelength	O
filters	O
as	O
short-pass	O
and	O
long-pass	O
to	O
avoid	O
confusion	O
,	O
which	O
would	O
correspond	O
to	O
high-pass	O
and	O
low-pass	B-Algorithm
frequencies	O
.	O
</s>
<s>
Low-pass	B-Algorithm
filters	I-Algorithm
exist	O
in	O
many	O
different	O
forms	O
,	O
including	O
electronic	O
circuits	O
such	O
as	O
a	O
hiss	B-Algorithm
filter	I-Algorithm
used	O
in	O
audio	O
,	O
anti-aliasing	O
filters	O
for	O
conditioning	O
signals	O
prior	O
to	O
analog-to-digital	O
conversion	O
,	O
digital	O
filters	O
for	O
smoothing	O
sets	O
of	O
data	O
,	O
acoustic	O
barriers	O
,	O
blurring	B-Error_Name
of	O
images	O
,	O
and	O
so	O
on	O
.	O
</s>
<s>
The	O
moving	O
average	O
operation	O
used	O
in	O
fields	O
such	O
as	O
finance	O
is	O
a	O
particular	O
kind	O
of	O
low-pass	B-Algorithm
filter	I-Algorithm
,	O
and	O
can	O
be	O
analyzed	O
with	O
the	O
same	O
signal	O
processing	O
techniques	O
as	O
are	O
used	O
for	O
other	O
low-pass	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
Low-pass	B-Algorithm
filters	I-Algorithm
provide	O
a	O
smoother	O
form	O
of	O
a	O
signal	O
,	O
removing	O
the	O
short-term	O
fluctuations	O
and	O
leaving	O
the	O
longer-term	O
trend	O
.	O
</s>
<s>
Filter	O
designers	O
will	O
often	O
use	O
the	O
low-pass	B-Algorithm
form	O
as	O
a	O
prototype	O
filter	O
.	O
</s>
<s>
The	O
desired	O
filter	O
is	O
obtained	O
from	O
the	O
prototype	O
by	O
scaling	O
for	O
the	O
desired	O
bandwidth	O
and	O
impedance	O
and	O
transforming	O
into	O
the	O
desired	O
bandform	O
(	O
that	O
is	O
low-pass	B-Algorithm
,	O
high-pass	O
,	O
band-pass	O
or	O
band-stop	O
)	O
.	O
</s>
<s>
Examples	O
of	O
low-pass	B-Algorithm
filters	I-Algorithm
occur	O
in	O
acoustics	O
,	O
optics	B-Algorithm
and	O
electronics	O
.	O
</s>
<s>
A	O
stiff	O
physical	O
barrier	O
tends	O
to	O
reflect	O
higher	O
sound	O
frequencies	O
,	O
and	O
so	O
acts	O
as	O
an	O
acoustic	O
low-pass	B-Algorithm
filter	I-Algorithm
for	O
transmitting	O
sound	O
.	O
</s>
<s>
An	O
optical	O
filter	O
with	O
the	O
same	O
function	O
can	O
correctly	O
be	O
called	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
,	O
but	O
conventionally	O
is	O
called	O
a	O
longpass	O
filter	O
(	O
low	O
frequency	O
is	O
long	O
wavelength	O
)	O
,	O
to	O
avoid	O
confusion	O
.	O
</s>
<s>
In	O
an	O
electronic	O
low-pass	B-Algorithm
RC	B-Algorithm
filter	I-Algorithm
for	O
voltage	O
signals	O
,	O
high	O
frequencies	O
in	O
the	O
input	O
signal	O
are	O
attenuated	O
,	O
but	O
the	O
filter	O
has	O
little	O
attenuation	O
below	O
the	O
cutoff	O
frequency	O
determined	O
by	O
its	O
RC	O
time	O
constant	O
.	O
</s>
<s>
Electronic	O
low-pass	B-Algorithm
filters	I-Algorithm
are	O
used	O
on	O
inputs	O
to	O
subwoofers	B-Application
and	O
other	O
types	O
of	O
loudspeakers	O
,	O
to	O
block	O
high	O
pitches	O
that	O
they	O
cannot	O
efficiently	O
reproduce	O
.	O
</s>
<s>
Radio	O
transmitters	O
use	O
low-pass	B-Algorithm
filters	I-Algorithm
to	O
block	O
harmonic	O
emissions	O
that	O
might	O
interfere	O
with	O
other	O
communications	O
.	O
</s>
<s>
The	O
tone	O
knob	O
on	O
many	O
electric	O
guitars	O
is	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
used	O
to	O
reduce	O
the	O
amount	O
of	O
treble	O
in	O
the	O
sound	O
.	O
</s>
<s>
An	O
integrator	O
is	O
another	O
time	O
constant	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Telephone	O
lines	O
fitted	O
with	O
DSL	B-Algorithm
splitters	I-Algorithm
use	O
low-pass	B-Algorithm
filters	I-Algorithm
to	O
separate	O
DSL	O
from	O
POTS	O
signals	O
(	O
and	O
high-pass	O
vice	O
versa	O
)	O
,	O
which	O
share	O
the	O
same	O
pair	O
of	O
wires	O
(	O
transmission	O
channel	O
)	O
.	O
</s>
<s>
Low-pass	B-Algorithm
filters	I-Algorithm
also	O
play	O
a	O
significant	O
role	O
in	O
the	O
sculpting	O
of	O
sound	O
created	O
by	O
analogue	O
and	O
virtual	O
analogue	O
synthesisers	O
.	O
</s>
<s>
A	O
low-pass	B-Algorithm
filter	I-Algorithm
is	O
used	O
as	O
an	O
anti-aliasing	O
filter	O
prior	O
to	O
sampling	B-Algorithm
and	O
for	O
reconstruction	O
in	O
digital-to-analog	O
conversion	O
.	O
</s>
<s>
An	O
ideal	B-Algorithm
low-pass	I-Algorithm
filter	I-Algorithm
completely	O
eliminates	O
all	O
frequencies	O
above	O
the	O
cutoff	O
frequency	O
while	O
passing	O
those	O
below	O
unchanged	O
;	O
its	O
frequency	O
response	O
is	O
a	O
rectangular	O
function	O
and	O
is	O
a	O
brick-wall	O
filter	O
.	O
</s>
<s>
The	O
transition	O
region	O
present	O
in	O
practical	O
filters	O
does	O
not	O
exist	O
in	O
an	O
ideal	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
An	O
ideal	B-Algorithm
low-pass	I-Algorithm
filter	I-Algorithm
can	O
be	O
realized	O
mathematically	O
(	O
theoretically	O
)	O
by	O
multiplying	O
a	O
signal	O
by	O
the	O
rectangular	O
function	O
in	O
the	O
frequency	O
domain	O
or	O
,	O
equivalently	O
,	O
convolution	B-Language
with	O
its	O
impulse	O
response	O
,	O
a	O
sinc	B-Algorithm
function	I-Algorithm
,	O
in	O
the	O
time	O
domain	O
.	O
</s>
<s>
However	O
,	O
the	O
ideal	B-Algorithm
filter	I-Algorithm
is	O
impossible	O
to	O
realize	O
without	O
also	O
having	O
signals	O
of	O
infinite	O
extent	O
in	O
time	O
,	O
and	O
so	O
generally	O
needs	O
to	O
be	O
approximated	O
for	O
real	O
ongoing	O
signals	O
,	O
because	O
the	O
sinc	B-Algorithm
function	I-Algorithm
's	O
support	O
region	O
extends	O
to	O
all	O
past	O
and	O
future	O
times	O
.	O
</s>
<s>
The	O
filter	O
would	O
therefore	O
need	O
to	O
have	O
infinite	O
delay	O
,	O
or	O
knowledge	O
of	O
the	O
infinite	O
future	O
and	O
past	O
,	O
in	O
order	O
to	O
perform	O
the	O
convolution	B-Language
.	O
</s>
<s>
Real	O
filters	O
for	O
real-time	B-General_Concept
applications	I-General_Concept
approximate	O
the	O
ideal	B-Algorithm
filter	I-Algorithm
by	O
truncating	O
and	O
windowing	B-Language
the	O
infinite	O
impulse	O
response	O
to	O
make	O
a	O
finite	O
impulse	O
response	O
;	O
applying	O
that	O
filter	O
requires	O
delaying	O
the	O
signal	O
for	O
a	O
moderate	O
period	O
of	O
time	O
,	O
allowing	O
the	O
computation	O
to	O
"	O
see	O
"	O
a	O
little	O
bit	O
into	O
the	O
future	O
.	O
</s>
<s>
An	O
ideal	B-Algorithm
low-pass	I-Algorithm
filter	I-Algorithm
results	O
in	O
ringing	B-Algorithm
artifacts	I-Algorithm
via	O
the	O
Gibbs	O
phenomenon	O
.	O
</s>
<s>
These	O
can	O
be	O
reduced	O
or	O
worsened	O
by	O
choice	O
of	O
windowing	B-Language
function	O
,	O
and	O
the	O
design	O
and	O
choice	O
of	O
real	O
filters	O
involves	O
understanding	O
and	O
minimizing	O
these	O
artifacts	O
.	O
</s>
<s>
For	O
example	O
,	O
"	O
simple	O
truncation	O
[	O
of	O
sinc ]	O
causes	O
severe	O
ringing	B-Algorithm
artifacts	I-Algorithm
,	O
"	O
in	O
signal	O
reconstruction	O
,	O
and	O
to	O
reduce	O
these	O
artifacts	O
one	O
uses	O
window	B-Language
functions	I-Language
"	O
which	O
drop	O
off	O
more	O
smoothly	O
at	O
the	O
edges.	O
"	O
</s>
<s>
The	O
Whittaker	O
–	O
Shannon	O
interpolation	O
formula	O
describes	O
how	O
to	O
use	O
a	O
perfect	O
low-pass	B-Algorithm
filter	I-Algorithm
to	O
reconstruct	O
a	O
continuous	O
signal	O
from	O
a	O
sampled	O
digital	O
signal	O
.	O
</s>
<s>
The	O
time	O
response	O
of	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
is	O
found	O
by	O
solving	O
the	O
response	O
to	O
the	O
simple	O
low-pass	B-Algorithm
RC	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
A	O
discrete	O
difference	O
equation	O
is	O
easily	O
obtained	O
by	O
sampling	B-Algorithm
the	O
step	O
input	O
response	O
above	O
at	O
regular	O
intervals	O
of	O
where	O
and	O
is	O
the	O
time	O
between	O
samples	O
.	O
</s>
<s>
Many	O
digital	O
filters	O
are	O
designed	O
to	O
give	O
low-pass	B-Algorithm
characteristics	O
.	O
</s>
<s>
Both	O
infinite	O
impulse	O
response	O
and	O
finite	O
impulse	O
response	O
low	B-Algorithm
pass	I-Algorithm
filters	I-Algorithm
as	O
well	O
as	O
filters	O
using	O
Fourier	B-Algorithm
transforms	I-Algorithm
are	O
widely	O
used	O
.	O
</s>
<s>
The	O
effect	O
of	O
an	O
infinite	O
impulse	O
response	O
low-pass	B-Algorithm
filter	I-Algorithm
can	O
be	O
simulated	O
on	O
a	O
computer	O
by	O
analyzing	O
an	O
RC	B-Algorithm
filter	I-Algorithm
's	O
behavior	O
in	O
the	O
time	O
domain	O
,	O
and	O
then	O
discretizing	O
the	O
model	O
.	O
</s>
<s>
The	O
expression	O
for	O
yields	O
the	O
equivalent	O
time	O
constant	O
in	O
terms	O
of	O
the	O
sampling	B-Algorithm
period	I-Algorithm
and	O
smoothing	O
factor	O
,	O
</s>
<s>
If	O
=	O
0.5	O
,	O
then	O
the	O
RC	O
time	O
constant	O
is	O
equal	O
to	O
the	O
sampling	B-Algorithm
period	I-Algorithm
.	O
</s>
<s>
If	O
,	O
then	O
RC	O
is	O
significantly	O
larger	O
than	O
the	O
sampling	B-Algorithm
interval	O
,	O
and	O
.	O
</s>
<s>
The	O
following	O
pseudocode	B-Language
algorithm	O
simulates	O
the	O
effect	O
of	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
on	O
a	O
series	O
of	O
digital	B-Algorithm
samples	I-Algorithm
:	O
</s>
<s>
//	O
Return	O
RC	O
low-pass	B-Algorithm
filter	I-Algorithm
output	O
samples	O
,	O
given	O
input	O
samples	O
,	O
</s>
<s>
The	O
loop	B-General_Concept
that	O
calculates	O
each	O
of	O
the	O
n	O
outputs	O
can	O
be	O
refactored	O
into	O
the	O
equivalent	O
:	O
</s>
<s>
This	O
filter	O
is	O
an	O
infinite-impulse-response	O
(	O
IIR	O
)	O
single-pole	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
Finite-impulse-response	O
filters	O
can	O
be	O
built	O
that	O
approximate	O
to	O
the	O
sinc	B-Algorithm
function	I-Algorithm
time-domain	O
response	O
of	O
an	O
ideal	O
sharp-cutoff	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
For	O
non-realtime	O
filtering	O
,	O
to	O
achieve	O
a	O
low	B-Algorithm
pass	I-Algorithm
filter	I-Algorithm
,	O
the	O
entire	O
signal	O
is	O
usually	O
taken	O
as	O
a	O
looped	O
signal	O
,	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
is	O
taken	O
,	O
filtered	O
in	O
the	O
frequency	O
domain	O
,	O
followed	O
by	O
an	O
inverse	O
Fourier	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
This	O
can	O
also	O
sometimes	O
be	O
done	O
in	O
real-time	B-General_Concept
,	O
where	O
the	O
signal	O
is	O
delayed	O
long	O
enough	O
to	O
perform	O
the	O
Fourier	B-Algorithm
transformation	I-Algorithm
on	O
shorter	O
,	O
overlapping	O
blocks	O
.	O
</s>
<s>
The	O
frequency	O
response	O
of	O
a	O
filter	O
is	O
generally	O
represented	O
using	O
a	O
Bode	B-Algorithm
plot	I-Algorithm
,	O
and	O
the	O
filter	O
is	O
characterized	O
by	O
its	O
cutoff	O
frequency	O
and	O
rate	O
of	O
frequency	O
rolloff	B-Algorithm
.	O
</s>
<s>
A	O
first-order	O
filter	O
,	O
for	O
example	O
,	O
reduces	O
the	O
signal	O
amplitude	O
by	O
half	O
(	O
so	O
power	O
reduces	O
by	O
a	O
factor	O
of	O
4	O
,	O
or	O
,	O
every	O
time	O
the	O
frequency	O
doubles	O
(	O
goes	O
up	O
one	O
octave	B-Language
)	O
;	O
more	O
precisely	O
,	O
the	O
power	O
rolloff	B-Algorithm
approaches	O
20dB	O
per	O
decade	B-Application
in	O
the	O
limit	O
of	O
high	O
frequency	O
.	O
</s>
<s>
The	O
magnitude	O
Bode	B-Algorithm
plot	I-Algorithm
for	O
a	O
first-order	O
filter	O
looks	O
like	O
a	O
horizontal	O
line	O
below	O
the	O
cutoff	O
frequency	O
,	O
and	O
a	O
diagonal	O
line	O
above	O
the	O
cutoff	O
frequency	O
.	O
</s>
<s>
If	O
the	O
transfer	O
function	O
of	O
a	O
first-order	O
low-pass	B-Algorithm
filter	I-Algorithm
has	O
a	O
zero	O
as	O
well	O
as	O
a	O
pole	O
,	O
the	O
Bode	B-Algorithm
plot	I-Algorithm
flattens	O
out	O
again	O
,	O
at	O
some	O
maximum	O
attenuation	O
of	O
high	O
frequencies	O
;	O
such	O
an	O
effect	O
is	O
caused	O
for	O
example	O
by	O
a	O
little	O
bit	O
of	O
the	O
input	O
leaking	O
around	O
the	O
one-pole	O
filter	O
;	O
this	O
one-pole	O
–	O
one-zero	O
filter	O
is	O
still	O
a	O
first-order	O
low-pass	B-Algorithm
.	O
</s>
<s>
See	O
Pole	B-Algorithm
–	I-Algorithm
zero	I-Algorithm
plot	I-Algorithm
and	O
RC	B-Algorithm
circuit	I-Algorithm
.	O
</s>
<s>
The	O
Bode	B-Algorithm
plot	I-Algorithm
for	O
this	O
type	O
of	O
filter	O
resembles	O
that	O
of	O
a	O
first-order	O
filter	O
,	O
except	O
that	O
it	O
falls	O
off	O
more	O
quickly	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
second-order	O
Butterworth	O
filter	O
reduces	O
the	O
signal	O
amplitude	O
to	O
one	O
fourth	O
its	O
original	O
level	O
every	O
time	O
the	O
frequency	O
doubles	O
(	O
so	O
power	O
decreases	O
by	O
12dB	O
per	O
octave	B-Language
,	O
or	O
40dB	O
per	O
decade	B-Application
)	O
.	O
</s>
<s>
Other	O
all-pole	O
second-order	O
filters	O
may	O
roll	B-Algorithm
off	I-Algorithm
at	O
different	O
rates	O
initially	O
depending	O
on	O
their	O
Q	O
factor	O
,	O
but	O
approach	O
the	O
same	O
final	O
rate	O
of	O
12dB	O
per	O
octave	B-Language
;	O
as	O
with	O
the	O
first-order	O
filters	O
,	O
zeroes	O
in	O
the	O
transfer	O
function	O
can	O
change	O
the	O
high-frequency	O
asymptote	B-Language
.	O
</s>
<s>
See	O
RLC	B-Algorithm
circuit	I-Algorithm
.	O
</s>
<s>
In	O
general	O
,	O
the	O
final	O
rate	O
of	O
power	O
rolloff	B-Algorithm
for	O
an	O
order	O
-	O
all-pole	O
filter	O
is	O
6	O
dB	O
per	O
octave	B-Language
(	O
20	O
dB	O
per	O
decade	B-Application
)	O
.	O
</s>
<s>
On	O
any	O
Butterworth	O
filter	O
,	O
if	O
one	O
extends	O
the	O
horizontal	O
line	O
to	O
the	O
right	O
and	O
the	O
diagonal	O
line	O
to	O
the	O
upper-left	O
(	O
the	O
asymptotes	B-Language
of	O
the	O
function	O
)	O
,	O
they	O
intersect	O
at	O
exactly	O
the	O
cutoff	O
frequency	O
,	O
3dB	O
below	O
the	O
horizontal	O
line	O
.	O
</s>
<s>
Many	O
second-order	O
filters	O
have	O
"	O
peaking	O
"	O
or	O
resonance	B-Application
that	O
puts	O
their	O
frequency	O
response	O
above	O
the	O
horizontal	O
line	O
at	O
this	O
peak	O
.	O
</s>
<s>
The	O
term	O
"	O
low-pass	B-Algorithm
filter	I-Algorithm
"	O
merely	O
refers	O
to	O
the	O
shape	O
of	O
the	O
filter	O
's	O
response	O
;	O
a	O
high-pass	O
filter	O
could	O
be	O
built	O
that	O
cuts	O
off	O
at	O
a	O
lower	O
frequency	O
than	O
any	O
low-pass	B-Algorithm
filter	I-Algorithm
—	O
it	O
is	O
their	O
responses	O
that	O
set	O
them	O
apart	O
.	O
</s>
<s>
(	O
In	O
discrete	O
time	O
,	O
one	O
can	O
similarly	O
consider	O
the	O
Z-transform	B-Algorithm
of	O
the	O
impulse	O
response	O
.	O
)	O
</s>
<s>
For	O
example	O
,	O
a	O
first-order	O
low-pass	B-Algorithm
filter	I-Algorithm
can	O
be	O
described	O
in	O
Laplace	O
notation	O
as	O
:	O
</s>
<s>
where	O
s	O
is	O
the	O
Laplace	O
transform	O
variable	O
,	O
τ	O
is	O
the	O
filter	O
time	O
constant	O
,	O
and	O
K	O
is	O
the	O
gain	O
of	O
the	O
filter	O
in	O
the	O
passband	B-Algorithm
.	O
</s>
<s>
One	O
simple	O
low-pass	B-Algorithm
filter	I-Algorithm
circuit	O
consists	O
of	O
a	O
resistor	O
in	O
series	O
with	O
a	O
load	O
,	O
and	O
a	O
capacitor	O
in	O
parallel	O
with	O
the	O
load	O
.	O
</s>
<s>
At	O
higher	O
frequencies	O
the	O
reactance	O
drops	O
,	O
and	O
the	O
capacitor	O
effectively	O
functions	O
as	O
a	O
short	B-Application
circuit	I-Application
.	O
</s>
<s>
It	O
is	O
the	O
Bode	B-Algorithm
plot	I-Algorithm
and	O
frequency	O
response	O
that	O
show	O
this	O
variability	O
.	O
</s>
<s>
A	O
resistor	O
–	O
inductor	O
circuit	O
or	O
RL	B-Algorithm
filter	I-Algorithm
is	O
an	O
electric	O
circuit	O
composed	O
of	O
resistors	O
and	O
inductors	O
driven	O
by	O
a	O
voltage	O
or	O
current	O
source	O
.	O
</s>
<s>
A	O
first	O
order	O
RL	B-Algorithm
circuit	I-Algorithm
is	O
composed	O
of	O
one	O
resistor	O
and	O
one	O
inductor	O
and	O
is	O
the	O
simplest	O
type	O
of	O
RL	B-Algorithm
circuit	I-Algorithm
.	O
</s>
<s>
A	O
first	O
order	O
RL	B-Algorithm
circuit	I-Algorithm
is	O
one	O
of	O
the	O
simplest	O
analogue	O
infinite	O
impulse	O
response	O
electronic	B-Architecture
filters	I-Architecture
.	O
</s>
<s>
An	O
RLC	B-Algorithm
circuit	I-Algorithm
(	O
the	O
letters	O
R	O
,	O
L	O
and	O
C	O
can	O
be	O
in	O
a	O
different	O
sequence	O
)	O
is	O
an	O
electrical	O
circuit	O
consisting	O
of	O
a	O
resistor	O
,	O
an	O
inductor	O
,	O
and	O
a	O
capacitor	O
,	O
connected	O
in	O
series	O
or	O
in	O
parallel	O
.	O
</s>
<s>
The	O
circuit	O
forms	O
a	O
harmonic	O
oscillator	O
for	O
current	O
and	O
will	O
resonate	B-Application
in	O
a	O
similar	O
way	O
as	O
an	O
LC	O
circuit	O
will	O
.	O
</s>
<s>
Another	O
important	O
application	O
is	O
for	O
tuning	B-Device
,	O
such	O
as	O
in	O
radio	O
receivers	B-Device
or	O
television	O
sets	O
,	O
where	O
they	O
are	O
used	O
to	O
select	O
a	O
narrow	O
range	O
of	O
frequencies	O
from	O
the	O
ambient	O
radio	O
waves	O
.	O
</s>
<s>
An	O
RLC	B-Algorithm
circuit	I-Algorithm
can	O
be	O
used	O
as	O
a	O
band-pass	O
filter	O
,	O
band-stop	O
filter	O
,	O
low-pass	B-Algorithm
filter	I-Algorithm
or	O
high-pass	O
filter	O
.	O
</s>
<s>
The	O
RLC	B-Algorithm
filter	I-Algorithm
is	O
described	O
as	O
a	O
second-order	O
circuit	O
,	O
meaning	O
that	O
any	O
voltage	O
or	O
current	O
in	O
the	O
circuit	O
can	O
be	O
described	O
by	O
a	O
second-order	O
differential	O
equation	O
in	O
circuit	O
analysis	O
.	O
</s>
<s>
Another	O
type	O
of	O
electrical	O
circuit	O
is	O
an	O
active	O
low-pass	B-Algorithm
filter	I-Algorithm
.	O
</s>
<s>
The	O
gain	O
in	O
the	O
passband	B-Algorithm
is	O
−	O
R2/R1	O
,	O
and	O
the	O
stopband	O
drops	O
off	O
at	O
−6dB	O
per	O
octave	B-Language
(	O
that	O
is	O
−20dB	O
per	O
decade	B-Application
)	O
as	O
it	O
is	O
a	O
first-order	O
filter	O
.	O
</s>
