<s>
Code-excited	B-Algorithm
linear	I-Algorithm
prediction	I-Algorithm
(	O
CELP	B-Algorithm
)	O
is	O
a	O
linear	B-Algorithm
predictive	I-Algorithm
speech	B-Application
coding	I-Application
algorithm	O
originally	O
proposed	O
by	O
Manfred	O
R	O
.	O
Schroeder	O
and	O
Bishnu	O
S	O
.	O
Atal	O
in	O
1985	O
.	O
</s>
<s>
At	O
the	O
time	O
,	O
it	O
provided	O
significantly	O
better	O
quality	O
than	O
existing	O
low	O
bit-rate	O
algorithms	O
,	O
such	O
as	O
residual-excited	B-Algorithm
linear	I-Algorithm
prediction	I-Algorithm
(	O
RELP	O
)	O
and	O
linear	B-Algorithm
predictive	I-Algorithm
coding	I-Algorithm
(	O
LPC	O
)	O
vocoders	B-Application
(	O
e.g.	O
,	O
FS-1015	O
)	O
.	O
</s>
<s>
Along	O
with	O
its	O
variants	O
,	O
such	O
as	O
algebraic	B-Algorithm
CELP	I-Algorithm
,	O
relaxed	B-Algorithm
CELP	I-Algorithm
,	O
low-delay	B-Algorithm
CELP	I-Algorithm
and	O
vector	B-Algorithm
sum	I-Algorithm
excited	I-Algorithm
linear	I-Algorithm
prediction	I-Algorithm
,	O
it	O
is	O
currently	O
the	O
most	O
widely	O
used	O
speech	B-Application
coding	I-Application
algorithm	O
.	O
</s>
<s>
It	O
is	O
also	O
used	O
in	O
MPEG-4	B-Algorithm
Audio	I-Algorithm
speech	B-Application
coding	I-Application
.	O
</s>
<s>
CELP	B-Algorithm
is	O
commonly	O
used	O
as	O
a	O
generic	O
term	O
for	O
a	O
class	O
of	O
algorithms	O
and	O
not	O
for	O
a	O
particular	O
codec	O
.	O
</s>
<s>
The	O
CELP	B-Algorithm
algorithm	O
is	O
based	O
on	O
four	O
main	O
ideas	O
:	O
</s>
<s>
Using	O
the	O
source-filter	B-Application
model	I-Application
of	I-Application
speech	I-Application
production	I-Application
through	O
linear	O
prediction	O
(	O
LP	O
)	O
(	O
see	O
the	O
textbook	O
"	O
speech	B-Application
coding	I-Application
algorithm	O
"	O
)	O
;	O
</s>
<s>
The	O
original	O
algorithm	O
as	O
simulated	O
in	O
1983	O
by	O
Schroeder	O
and	O
Atal	O
required	O
150	O
seconds	O
to	O
encode	O
1	O
second	O
of	O
speech	O
when	O
run	O
on	O
a	O
Cray-1	B-Device
supercomputer	O
.	O
</s>
<s>
Before	O
exploring	O
the	O
complex	O
encoding	O
process	O
of	O
CELP	B-Algorithm
we	O
introduce	O
the	O
decoder	O
here	O
.	O
</s>
<s>
Figure	O
1	O
describes	O
a	O
generic	O
CELP	B-Algorithm
decoder	O
.	O
</s>
<s>
The	O
fixed	O
codebook	O
is	O
a	O
vector	B-Algorithm
quantization	I-Algorithm
dictionary	O
that	O
is	O
(	O
implicitly	O
or	O
explicitly	O
)	O
hard-coded	O
into	O
the	O
codec	O
.	O
</s>
<s>
This	O
codebook	O
can	O
be	O
algebraic	O
(	O
ACELP	B-Algorithm
)	O
or	O
be	O
stored	O
explicitly	O
(	O
e.g.	O
</s>
<s>
Speex	B-Application
)	O
.	O
</s>
<s>
The	O
filter	O
that	O
shapes	O
the	O
excitation	O
has	O
an	O
all-pole	O
model	O
of	O
the	O
form	O
,	O
where	O
is	O
called	O
the	O
prediction	O
filter	O
and	O
is	O
obtained	O
using	O
linear	O
prediction	O
(	O
Levinson	B-Algorithm
–	I-Algorithm
Durbin	I-Algorithm
algorithm	I-Algorithm
)	O
.	O
</s>
<s>
The	O
main	O
principle	O
behind	O
CELP	B-Algorithm
is	O
called	O
analysis-by-synthesis	B-Application
(	O
AbS	O
)	O
and	O
means	O
that	O
the	O
encoding	O
(	O
analysis	O
)	O
is	O
performed	O
by	O
perceptually	O
optimizing	O
the	O
decoded	O
(	O
synthesis	O
)	O
signal	O
in	O
a	O
closed	O
loop	O
.	O
</s>
<s>
In	O
theory	O
,	O
the	O
best	O
CELP	B-Algorithm
stream	O
would	O
be	O
produced	O
by	O
trying	O
all	O
possible	O
bit	O
combinations	O
and	O
selecting	O
the	O
one	O
that	O
produces	O
the	O
best-sounding	O
decoded	O
signal	O
.	O
</s>
<s>
In	O
order	O
to	O
achieve	O
real-time	O
encoding	O
using	O
limited	O
computing	O
resources	O
,	O
the	O
CELP	B-Algorithm
search	O
is	O
broken	O
down	O
into	O
smaller	O
,	O
more	O
manageable	O
,	O
sequential	O
searches	O
using	O
a	O
simple	O
perceptual	O
weighting	O
function	O
.	O
</s>
<s>
Linear	B-Algorithm
prediction	I-Algorithm
coefficients	I-Algorithm
(	O
LPC	O
)	O
are	O
computed	O
and	O
quantized	O
,	O
usually	O
as	O
line	B-Algorithm
spectral	I-Algorithm
pairs	I-Algorithm
(	O
LSPs	O
)	O
.	O
</s>
<s>
That	O
's	O
why	O
instead	O
of	O
minimizing	O
the	O
simple	O
quadratic	O
error	O
,	O
CELP	B-Algorithm
minimizes	O
the	O
error	O
for	O
the	O
perceptually	O
weighted	O
domain	O
.	O
</s>
<s>
The	O
weighting	O
filter	O
W(z )	O
is	O
typically	O
derived	O
from	O
the	O
LPC	O
filter	O
by	O
the	O
use	O
of	O
bandwidth	B-Algorithm
expansion	I-Algorithm
:	O
</s>
