<s>
Common	B-Algorithm
spatial	I-Algorithm
pattern	I-Algorithm
(	O
CSP	O
)	O
is	O
a	O
mathematical	O
procedure	O
used	O
in	O
signal	O
processing	O
for	O
separating	O
a	O
multivariate	O
signal	O
into	O
additive	O
subcomponents	O
which	O
have	O
maximum	O
differences	O
in	O
variance	O
between	O
two	O
windows	O
.	O
</s>
<s>
The	O
solution	O
is	O
given	O
by	O
computing	O
the	O
two	O
covariance	O
matrices	B-Architecture
:	O
</s>
<s>
Then	O
,	O
the	O
simultaneous	O
diagonalization	O
of	O
those	O
two	O
matrices	B-Architecture
(	O
also	O
called	O
generalized	O
eigenvalue	O
decomposition	O
)	O
is	O
realized	O
.	O
</s>
<s>
We	O
find	O
the	O
matrix	O
of	O
eigenvectors	O
and	O
the	O
diagonal	B-Algorithm
matrix	I-Algorithm
of	O
eigenvalues	O
sorted	O
by	O
decreasing	O
order	O
such	O
that	O
:	O
</s>
<s>
with	O
the	O
identity	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
Since	O
the	O
matrix	O
depends	O
only	O
of	O
the	O
covariance	O
matrices	B-Architecture
,	O
the	O
same	O
results	O
can	O
be	O
obtained	O
if	O
the	O
processing	O
is	O
applied	O
on	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
the	O
signals	O
.	O
</s>
<s>
Y	O
.	O
Wang	O
has	O
proposed	O
a	O
particular	O
choice	O
for	O
the	O
first	O
window	B-Language
in	O
order	O
to	O
extract	O
components	O
which	O
have	O
a	O
specific	O
period	O
.	O
</s>
<s>
If	O
there	O
is	O
only	O
one	O
window	B-Language
,	O
can	O
be	O
considered	O
as	O
the	O
identity	B-Algorithm
matrix	I-Algorithm
and	O
then	O
CSP	O
corresponds	O
to	O
Principal	B-Application
component	I-Application
analysis	I-Application
.	O
</s>
<s>
Linear	B-General_Concept
discriminant	I-General_Concept
analysis	I-General_Concept
(	O
LDA	O
)	O
and	O
CSP	O
apply	O
in	O
different	O
circumstances	O
.	O
</s>
<s>
Thus	O
CSP	O
is	O
good	O
,	O
for	O
example	O
,	O
in	O
separating	O
the	O
signal	O
from	O
the	O
noise	O
in	O
an	O
event-related	B-Algorithm
potential	I-Algorithm
(	O
ERP	O
)	O
experiment	O
because	O
both	O
distributions	O
have	O
zero	O
mean	O
and	O
there	O
is	O
no	O
distinction	O
for	O
LDA	O
to	O
separate	O
.	O
</s>
<s>
The	O
CSP	O
method	O
can	O
be	O
applied	O
to	O
multivariate	O
signals	O
in	O
generally	O
,	O
is	O
commonly	O
found	O
in	O
application	O
to	O
electroencephalographic	B-Application
(	O
EEG	B-Application
)	O
signals	O
.	O
</s>
<s>
Particularly	O
,	O
the	O
method	O
is	O
often	O
used	O
in	O
brain	B-Application
–	I-Application
computer	I-Application
interfaces	I-Application
to	O
retrieve	O
the	O
component	O
signals	O
which	O
best	O
transduce	O
the	O
cerebral	O
activity	O
for	O
a	O
specific	O
task	O
(	O
e.g.	O
</s>
<s>
It	O
can	O
also	O
be	O
used	O
to	O
separate	O
artifacts	O
from	O
EEG	B-Application
signals	O
.	O
</s>
<s>
CSP	O
can	O
be	O
adapted	O
for	O
the	O
analysis	O
of	O
the	O
event-related	B-Algorithm
potentials	I-Algorithm
.	O
</s>
