<s>
In	O
signal	O
processing	O
,	O
the	O
overlap	B-Algorithm
–	I-Algorithm
add	I-Algorithm
method	I-Algorithm
is	O
an	O
efficient	O
way	O
to	O
evaluate	O
the	O
discrete	O
convolution	B-Language
of	O
a	O
very	O
long	O
signal	O
with	O
a	O
finite	O
impulse	O
response	O
(	O
FIR	O
)	O
filter	O
:	O
</s>
<s>
This	O
article	O
uses	O
common	O
abstract	O
notations	O
,	O
such	O
as	O
or	O
in	O
which	O
it	O
is	O
understood	O
that	O
the	O
functions	O
should	O
be	O
thought	O
of	O
in	O
their	O
totality	O
,	O
rather	O
than	O
at	O
specific	O
instants	O
(	O
see	O
Convolution	B-Language
#Notation	O
)	O
.	O
</s>
<s>
The	O
concept	O
is	O
to	O
divide	O
the	O
problem	O
into	O
multiple	O
convolutions	B-Language
of	O
h[n]	O
with	O
short	O
segments	O
of	O
:	O
</s>
<s>
and	O
y[n]	O
can	O
be	O
written	O
as	O
a	O
sum	O
of	O
short	O
convolutions	B-Language
:	O
</s>
<s>
where	O
the	O
linear	O
convolution	B-Language
is	O
zero	O
outside	O
the	O
region	O
.	O
</s>
<s>
And	O
for	O
any	O
parameter	O
it	O
is	O
equivalent	O
to	O
the	O
N-point	O
circular	B-Algorithm
convolution	I-Algorithm
of	O
with	O
in	O
the	O
.	O
</s>
<s>
The	O
advantage	O
is	O
that	O
the	O
circular	B-Algorithm
convolution	I-Algorithm
can	O
be	O
computed	O
more	O
efficiently	O
than	O
linear	O
convolution	B-Language
,	O
according	O
to	O
the	O
circular	B-Algorithm
convolution	I-Algorithm
theorem	O
:	O
</s>
<s>
The	O
following	O
is	O
a	O
pseudocode	B-Language
of	O
the	O
algorithm	O
:	O
</s>
<s>
When	O
the	O
DFT	O
and	O
IDFT	O
are	O
implemented	O
by	O
the	O
FFT	O
algorithm	O
,	O
the	O
pseudocode	B-Language
above	O
requires	O
about	O
complex	O
multiplications	O
for	O
the	O
FFT	O
,	O
product	O
of	O
arrays	O
,	O
and	O
IFFT	O
.	O
</s>
<s>
Comparatively	O
,	O
the	O
number	O
of	O
complex	O
multiplications	O
required	O
by	O
the	O
pseudocode	B-Language
algorithm	O
is	O
:	O
</s>
<s>
Hence	O
the	O
cost	O
of	O
the	O
overlap	B-Algorithm
–	I-Algorithm
add	I-Algorithm
method	I-Algorithm
scales	O
almost	O
as	O
while	O
the	O
cost	O
of	O
a	O
single	O
,	O
large	O
circular	B-Algorithm
convolution	I-Algorithm
is	O
almost	O
.	O
</s>
<s>
When	O
the	O
overlap-add	B-Algorithm
method	I-Algorithm
is	O
faster	O
,	O
the	O
ratio	O
exceeds	O
1	O
,	O
and	O
ratios	O
as	O
high	O
as	O
3	O
are	O
seen	O
.	O
</s>
