Databases Reference
In-Depth Information
The unlocked scale factor is adapted using the Jayant algorithm with one slight modifica-
tion. If we were to use the Jayant algorithm, the unlocked scale factor could be adapted as
α
u
(
)
=
α
k
−
1
M
[
I
k
−
1
]
(62)
k
where
M
[·]
is the multiplier. In terms of logarithms, this becomes
y
u
(
k
)
=
y
(
k
−
1
)
+
log
M
[
I
k
−
1
]
(63)
The modification consists of introducing some memory into the adaptive process so that the
encoder and decoder converge following transmission errors:
y
u
(
k
)
=
(
1
−
)
y
(
k
−
1
)
+
W
[
I
k
−
1
]
(64)
2
−
5
.
The locked scale factor is obtained from the unlocked scale factor through
where
W
[·] =
log
M
[·]
, and
=
2
−
6
y
l
(
k
)
=
(
1
−
γ)
y
l
(
k
−
1
)
+
γ
y
u
(
k
),
γ
=
(65)
The Predictor
The recommended predictor is a backward adaptive predictor that uses a linear combination
of the past two reconstructed values as well as the six past quantized differences to generate
the prediction:
2
6
a
(
k
−
1
)
i
b
(
k
−
1
)
i
d
k
−
i
p
k
=
x
k
−
i
+
ˆ
(66)
i
=
1
i
=
1
The set of predictor coefficients is updated using a simplified form of the LMS algorithm:
a
(
k
)
1
a
(
k
−
1
)
1
2
−
8
2
−
8
sgn
=
(
1
−
)
+
3
×
[
z
(
k
)
]
sgn
[
z
(
k
−
1
)
]
(67)
a
(
k
)
2
a
(
k
−
1
)
2
2
−
7
2
−
7
=
(
1
−
)
+
(
sgn
[
z
(
k
)
]
sgn
[
z
(
k
−
2
)
]
f
a
(
k
−
1
)
1
−
sgn
[
z
(
k
)
]
sgn
[
z
(
k
−
1
)
]
)
(68)
where
6
)
=
d
k
+
b
(
k
−
1
)
i
d
k
−
i
z
(
k
(69)
i
=
1
4
1
2
β
|
β
|
f
(β)
=
(70)
1
2
(β)
|
β
|
>
2sgn
The coefficients
{
b
i
}
are updated using the following equation:
b
(
k
)
i
b
(
k
−
1
)
i
2
−
8
2
−
7
sgn
[
d
k
]
[
d
k
−
i
]
=
(
1
−
)
+
sgn
(71)
Notice that in the adaptive algorithms we have replaced products of reconstructed values
and products of quantizer outputs with products of their signs. This is computationally much
simpler and does not lead to any significant degradation of the adaptation process. Furthermore,
the values of the coefficients are selected such that multiplication with these coefficients can
