<s>
Bandwidth	B-Algorithm
expansion	I-Algorithm
is	O
a	O
technique	O
for	O
widening	O
the	O
bandwidth	B-Algorithm
or	O
the	O
resonances	B-Application
in	O
an	O
LPC	B-Algorithm
filter	O
.	O
</s>
<s>
The	O
bandwidth-expanded	O
filter	O
can	O
be	O
easily	O
derived	O
from	O
the	O
original	O
filter	O
by	O
:	O
</s>
<s>
The	O
bandwidth-expanded	O
filter	O
can	O
be	O
expressed	O
as	O
:	O
</s>
<s>
In	O
other	O
words	O
,	O
each	O
coefficient	O
in	O
the	O
original	O
filter	O
is	O
simply	O
multiplied	O
by	O
in	O
the	O
bandwidth-expanded	O
filter	O
.	O
</s>
<s>
The	O
simplicity	O
of	O
this	O
transformation	O
makes	O
it	O
attractive	O
,	O
especially	O
in	O
CELP	B-Algorithm
coding	O
of	O
speech	O
,	O
where	O
it	O
is	O
often	O
used	O
for	O
the	O
perceptual	O
noise	O
weighting	O
and/or	O
to	O
stabilize	O
the	O
LPC	B-Algorithm
analysis	O
.	O
</s>
<s>
However	O
,	O
when	O
it	O
comes	O
to	O
stabilizing	O
the	O
LPC	B-Algorithm
analysis	O
,	O
lag	O
windowing	O
is	O
often	O
preferred	O
to	O
bandwidth	B-Algorithm
expansion	I-Algorithm
.	O
</s>
