Digital Signal Processing Reference
In-Depth Information
can be interpreted as the angle (Ox
,
OM
1
)
−
(Ox
,
OM
2
)=
−
(OM
1
,
OM
2
).We
introduce the
Overall Phase Difference
:
X
t
1
(
b
)
S
∗
(
b
)
OPD(
b
)=arg
{
}
which has an interpretation in the complex plane given in Figure 9.3. We can see that
if we set Φ
1
=OPDand Φ
2
=OPD
ICPD, we obtain
X
1
and
X
2
at the receiver
aligned “on average” with
X
1
and
X
2
at the transmitter.
−
Knowing
X
1
and
X
2
, two overlap-add syntheses, one for each channel, enables
the calculation of
x
1
(
n
) and
x
2
(
n
).
9.4.4.
Information transmitted via the channel
For each tile of the time/frequency decomposition, the ICLD, ICPD, ICC, and
a
priori
the OPD must be transmitted. In reality, transmitting the OPD is not necessary.
In effect, if we realize a passive
downmixing
S
=
X
1
+
X
2
, Lapierre and Lefebvre
[LAP 06] have shown that:
OPD = arg
X
t
1
(
X
1
+
X
2
)
=arg
||
exp(
j
ICPD)
X
1
||
2
+
X
t
1
X
2
|
|
OPD = arg
||
exp(
j
ICPD)
X
t
1
X
2
|
X
1
||
+
|
||
X
2
||
||
X
1
|| ||
X
2
||
OPD = arg
{
c
+ICCexp(
j
ICPD)
}
This result can be immediately generalized to the case of an active
downmix
.
In effect:
OPD = arg
X
t
1
[cos(
θ
)
X
1
+ sin(
θ
)
X
2
]
OPD = arg
cos(
θ
)
||
exp(
j
ICPD)
X
t
1
X
2
|
X
1
||
|
+ sin(
θ
)
||
X
2
||
||
X
1
|| ||
X
2
||
OPD = arg
{
cos(
θ
)
c
+ sin(
θ
)ICCexp(
j
ICPD)
}
9.5. Draft International Standard
The document [INT 05] shows that in reality there is no active
downmix
.The
monophonic signal is directly given by
s
(
n
)=[
x
1
(
n
)+
x
2
(
n
)]
/
2.
In Table 9.1, the quantization code books for the ICLD, ICPD, and ICC parameters
are presented. Apparently, the OPD is also quantized with the ICPD code book
and transmitted. Under the hypothesis in which only the first three parameters are
