<s>
Roll-off	B-Algorithm
is	O
the	O
steepness	O
of	O
a	O
transfer	O
function	O
with	O
frequency	O
,	O
particularly	O
in	O
electrical	O
network	O
analysis	O
,	O
and	O
most	O
especially	O
in	O
connection	O
with	O
filter	O
circuits	O
in	O
the	O
transition	O
between	O
a	O
passband	B-Algorithm
and	O
a	O
stopband	O
.	O
</s>
<s>
It	O
is	O
usual	O
to	O
measure	O
roll-off	B-Algorithm
as	O
a	O
function	O
of	O
logarithmic	O
frequency	O
;	O
consequently	O
,	O
the	O
units	O
of	O
roll-off	B-Algorithm
are	O
either	O
decibels	O
per	O
decade	B-Application
(	O
dB/decade	O
)	O
,	O
where	O
a	O
decade	B-Application
is	O
a	O
tenfold	O
increase	O
in	O
frequency	O
,	O
or	O
decibels	O
per	O
octave	O
(	O
dB/8ve	O
)	O
,	O
where	O
an	O
octave	O
is	O
a	O
twofold	O
increase	O
in	O
frequency	O
.	O
</s>
<s>
The	O
concept	O
of	O
roll-off	B-Algorithm
stems	O
from	O
the	O
fact	O
that	O
in	O
many	O
networks	O
roll-off	B-Algorithm
tends	O
towards	O
a	O
constant	O
gradient	O
at	O
frequencies	O
well	O
away	O
from	O
the	O
cut-off	O
point	O
of	O
the	O
frequency	O
curve	O
.	O
</s>
<s>
Roll-off	B-Algorithm
enables	O
the	O
cut-off	O
performance	O
of	O
such	O
a	O
filter	O
network	O
to	O
be	O
reduced	O
to	O
a	O
single	O
number	O
.	O
</s>
<s>
Note	O
that	O
roll-off	B-Algorithm
can	O
occur	O
with	O
decreasing	O
frequency	O
as	O
well	O
as	O
increasing	O
frequency	O
,	O
depending	O
on	O
the	O
bandform	O
of	O
the	O
filter	O
being	O
considered	O
:	O
for	O
instance	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
will	O
roll-off	B-Algorithm
with	O
increasing	O
frequency	O
,	O
but	O
a	O
high-pass	O
filter	O
or	O
the	O
lower	O
stopband	O
of	O
a	O
band-pass	O
filter	O
will	O
roll-off	B-Algorithm
with	O
decreasing	O
frequency	O
.	O
</s>
<s>
For	O
brevity	O
,	O
this	O
article	O
describes	O
only	O
low-pass	B-Algorithm
filters	I-Algorithm
.	O
</s>
<s>
A	O
simple	O
first-order	O
network	O
such	O
as	O
a	O
RC	B-Algorithm
circuit	I-Algorithm
will	O
have	O
a	O
roll-off	B-Algorithm
of	O
20dB/decade	O
.	O
</s>
<s>
This	O
is	O
approximately	O
equal	O
(	O
to	O
within	O
normal	O
engineering	O
required	O
accuracy	O
)	O
to	O
6dB/octave	O
and	O
is	O
the	O
more	O
usual	O
description	O
given	O
for	O
this	O
roll-off	B-Algorithm
.	O
</s>
<s>
This	O
can	O
be	O
shown	O
to	O
be	O
so	O
by	O
considering	O
the	O
voltage	O
transfer	O
function	O
,	O
A	O
,	O
of	O
the	O
RC	B-Algorithm
network	I-Algorithm
:	O
</s>
<s>
Roll-off	B-Algorithm
is	O
given	O
by	O
,	O
</s>
<s>
For	O
a	O
decade	B-Application
this	O
is	O
;	O
</s>
<s>
consequently	O
,	O
the	O
total	O
roll-off	B-Algorithm
is	O
given	O
by	O
,	O
</s>
<s>
For	O
some	O
filter	O
classes	O
,	O
such	O
as	O
the	O
Butterworth	O
filter	O
,	O
the	O
insertion	O
loss	O
is	O
still	O
monotonically	O
increasing	O
with	O
frequency	O
and	O
quickly	O
asymptotically	B-Language
converges	O
to	O
a	O
roll-off	B-Algorithm
of	O
6ndB/8ve	O
,	O
but	O
in	O
others	O
,	O
such	O
as	O
the	O
Chebyshev	O
or	O
elliptic	O
filter	O
the	O
roll-off	B-Algorithm
near	O
the	O
cut-off	O
frequency	O
is	O
much	O
faster	O
and	O
elsewhere	O
the	O
response	O
is	O
anything	O
but	O
monotonic	O
.	O
</s>
<s>
Nevertheless	O
,	O
all	O
filter	O
classes	O
eventually	O
converge	O
to	O
a	O
roll-off	B-Algorithm
of	O
6ndB/8ve	O
theoretically	O
at	O
some	O
arbitrarily	O
high	O
frequency	O
,	O
but	O
in	O
many	O
applications	O
this	O
will	O
occur	O
in	O
a	O
frequency	O
band	O
of	O
no	O
interest	O
to	O
the	O
application	O
and	O
parasitic	O
effects	O
may	O
well	O
start	O
to	O
dominate	O
long	O
before	O
this	O
happens	O
.	O
</s>
<s>
Filters	O
with	O
a	O
high	O
roll-off	B-Algorithm
were	O
first	O
developed	O
to	O
prevent	O
crosstalk	O
between	O
adjacent	O
channels	O
on	O
telephone	O
FDM	B-Protocol
systems	O
.	O
</s>
<s>
Roll-off	B-Algorithm
is	O
also	O
significant	O
on	O
audio	O
loudspeaker	O
crossover	B-Algorithm
filters	I-Algorithm
:	O
here	O
the	O
need	O
is	O
not	O
so	O
much	O
for	O
a	O
high	O
roll-off	B-Algorithm
but	O
that	O
the	O
roll-offs	B-Algorithm
of	O
the	O
high	O
frequency	O
and	O
low-frequency	O
sections	O
are	O
symmetrical	O
and	O
complementary	O
.	O
</s>
<s>
An	O
interesting	O
need	O
for	O
high	O
roll-off	B-Algorithm
arises	O
in	O
EEG	B-Application
machines	O
.	O
</s>
<s>
Here	O
the	O
filters	O
mostly	O
make	O
do	O
with	O
a	O
basic	O
6dB/8ve	O
roll-off	B-Algorithm
,	O
however	O
,	O
some	O
instruments	O
provide	O
a	O
switchable	O
35	O
Hz	O
filter	O
at	O
the	O
high	O
frequency	O
end	O
with	O
a	O
faster	O
roll-off	B-Algorithm
to	O
help	O
filter	O
out	O
noise	O
generated	O
by	O
muscle	O
activity	O
.	O
</s>
