Digital Signal Processing Reference
In-Depth Information
x
(
n
)
r
(
n
)
1
p
(
n
)
A
(
z
)
A
(
z
/
g
)
0
-
p
(
n
)
1
L
-
Min ||
p
-
p
||
0
1
C
++
A
(
z
/
g
)
p
N
- 1
bz
-
Q
Figure 6.9.
Short-term and long-term prediction
gains
g
k
so that the vector
k
=1
g
k
c
j
(
k
)
,whenfilteredbythefilter1
/B
(
z
) and then
the perceptual filter 1
/A
(
z/γ
), results in the modeled vector
p
which is the closest
possible resemblance of the vector
p
. We have seen that the modeled perceptual signal
is written as:
n
∞
p
(
n
)=
h
(
i
)
y
(
n
−
i
)+
h
(
i
)
y
(
n
−
i
) or
n
=0
···
N
−
1
i
=0
i
=
n
+1
0,whichis
apriori
unknown, is composed of an unknown part
which depends only on
c
j
(
k
)
and
g
k
and a known part:
But
y
(
n
) for
n
≥
K
g
k
c
j
(
k
)
(
n
)+
by
(
n
y
(
n
)=
−
Q
)
k
=1
if we allow the hypothesis that the long-term predictor parameters
b
and
Q
have been
determined and that:
n − Q<
0
∀n ∈
0
···N −
1
that is:
Q
≥
N
The delay
Q
must therefore be greater than or equal to the analysis frame size.
Finally, the modeled perceptual signal is written as:
K
n
n
∞
h
(
i
)
c
j
(
k
)
(
n−i
)+
b
p
(
n
)=
g
k
h
(
i
)
y
(
n−i−Q
)+
h
(
i
)
y
(
n−i
)
k
=1
i
=0
i
=0
i
=
n
+1
We can write:
p
k
=[
p
k
(0)
p
k
(
N
1)]
t
···
−
