<s>
In	O
signal	O
processing	O
,	O
signal	B-Algorithm
subspace	I-Algorithm
methods	O
are	O
empirical	O
linear	O
methods	O
for	O
dimensionality	B-Algorithm
reduction	I-Algorithm
and	O
noise	O
reduction	O
.	O
</s>
<s>
The	O
signal	B-Algorithm
subspace	I-Algorithm
is	O
also	O
used	O
in	O
radio	B-Device
direction	I-Device
finding	I-Device
using	O
the	O
MUSIC	O
(	O
algorithm	O
)	O
.	O
</s>
<s>
Essentially	O
the	O
methods	O
represent	O
the	O
application	O
of	O
a	O
principal	B-Application
components	I-Application
analysis	I-Application
(	O
PCA	O
)	O
approach	O
to	O
ensembles	O
of	O
observed	O
time-series	O
obtained	O
by	O
sampling	B-Algorithm
,	O
for	O
example	O
sampling	B-Algorithm
an	O
audio	O
signal	O
.	O
</s>
<s>
The	O
vector	O
space	O
spanned	O
by	O
the	O
basis	O
vectors	O
identified	O
by	O
the	O
analysis	O
is	O
then	O
the	O
signal	B-Algorithm
subspace	I-Algorithm
.	O
</s>
<s>
By	O
projecting	O
a	O
sample	O
on	O
a	O
signal	B-Algorithm
subspace	I-Algorithm
,	O
that	O
is	O
,	O
keeping	O
only	O
the	O
component	O
of	O
the	O
sample	O
that	O
is	O
in	O
the	O
signal	B-Algorithm
subspace	I-Algorithm
defined	O
by	O
linear	O
combinations	O
of	O
the	O
first	O
few	O
most	O
energized	O
basis	O
vectors	O
,	O
and	O
throwing	O
away	O
the	O
rest	O
of	O
the	O
sample	O
,	O
which	O
is	O
in	O
the	O
remainder	O
of	O
the	O
space	O
orthogonal	O
to	O
this	O
subspace	O
,	O
a	O
certain	O
amount	O
of	O
noise	O
filtering	O
is	O
then	O
obtained	O
.	O
</s>
<s>
Signal	B-Algorithm
subspace	I-Algorithm
noise-reduction	O
can	O
be	O
compared	O
to	O
Wiener	O
filter	O
methods	O
.	O
</s>
<s>
The	O
basis	O
signals	O
used	O
in	O
Wiener	O
filtering	O
are	O
usually	O
harmonic	O
sine	O
waves	O
,	O
into	O
which	O
a	O
signal	O
can	O
be	O
decomposed	O
by	O
Fourier	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
In	O
contrast	O
,	O
the	O
basis	O
signals	O
used	O
to	O
construct	O
the	O
signal	B-Algorithm
subspace	I-Algorithm
are	O
identified	O
empirically	O
,	O
and	O
may	O
for	O
example	O
be	O
chirps	B-Application
,	O
or	O
particular	O
characteristic	O
shapes	O
of	O
transients	O
after	O
particular	O
triggering	O
events	O
,	O
rather	O
than	O
pure	O
sinusoids	O
.	O
</s>
<s>
In	O
contrast	O
,	O
the	O
signal	B-Algorithm
subspace	I-Algorithm
approach	O
represents	O
a	O
sharp	O
cut-off	O
:	O
an	O
orthogonal	O
component	O
either	O
lies	O
within	O
the	O
signal	B-Algorithm
subspace	I-Algorithm
,	O
in	O
which	O
case	O
it	O
is	O
100%	O
accepted	O
,	O
or	O
orthogonal	O
to	O
it	O
,	O
in	O
which	O
case	O
it	O
is	O
100%	O
rejected	O
.	O
</s>
<s>
In	O
the	O
simplest	O
case	O
signal	B-Algorithm
subspace	I-Algorithm
methods	O
assume	O
white	O
noise	O
,	O
but	O
extensions	O
of	O
the	O
approach	O
to	O
colored	O
noise	O
removal	O
and	O
the	O
evaluation	O
of	O
the	O
subspace-based	O
speech	O
enhancement	O
for	O
robust	O
speech	O
recognition	O
have	O
also	O
been	O
reported	O
.	O
</s>
