<s>
In	O
signal	O
processing	O
,	O
a	O
causal	B-Algorithm
filter	I-Algorithm
is	O
a	O
linear	O
and	O
time-invariant	O
causal	O
system	O
.	O
</s>
<s>
that	O
operate	O
in	O
real	B-General_Concept
time	I-General_Concept
)	O
must	O
be	O
causal	O
because	O
such	O
systems	O
cannot	O
act	O
on	O
a	O
future	O
input	O
.	O
</s>
<s>
If	O
shortening	O
is	O
necessary	O
,	O
it	O
is	O
often	O
accomplished	O
as	O
the	O
product	O
of	O
the	O
impulse-response	O
with	O
a	O
window	B-Language
function	I-Language
.	O
</s>
<s>
An	O
example	O
of	O
an	O
anti-causal	B-Algorithm
filter	I-Algorithm
is	O
a	O
maximum	O
phase	O
filter	O
,	O
which	O
can	O
be	O
defined	O
as	O
a	O
stable	O
,	O
anti-causal	B-Algorithm
filter	I-Algorithm
whose	O
inverse	O
is	O
also	O
stable	O
and	O
anti-causal	O
.	O
</s>
<s>
Let	O
h(t )	O
be	O
a	O
causal	B-Algorithm
filter	I-Algorithm
with	O
corresponding	O
Fourier	O
transform	O
H(ω )	O
.	O
</s>
<s>
where	O
is	O
a	O
Hilbert	B-Algorithm
transform	I-Algorithm
done	O
in	O
the	O
frequency	O
domain	O
(	O
rather	O
than	O
the	O
time	O
domain	O
)	O
.	O
</s>
<s>
Taking	O
the	O
Hilbert	B-Algorithm
transform	I-Algorithm
of	O
the	O
above	O
equation	O
yields	O
this	O
relation	O
between	O
"	O
H	O
"	O
and	O
its	O
Hilbert	B-Algorithm
transform	I-Algorithm
:	O
</s>
