Graphics Reference
In-Depth Information
Tabl e 6. 2
Scaling in
different stages for the 2D
forward transform
Scale factor
2
(6 C
M
/2)
First forward transform stage
2
(
B
C
M
9)
After the first forward transform stage (
S
TI
)
2
(6 C
M
/2)
Second forward transform stage
2
(
M
C 6)
After the second forward transform stage (
S
T
2
)
2
(15
B
M
)
Total scaling for the forward transform
Tabl e 6. 3
Scaling in
different stages for the 2D
inverse transform
Scale factor
2
(6 C
M
/2)
First inverse transform stage
2
7
After the first inverse transform stage (
S
ITI
)
2
(6 C
M
/2)
Second inverse transform stage
2
(20
B
)
After the second inverse transform stage (
S
IT
2
)
2
(15
B
M
)
Total scaling for the inverse transform
Finally, two useful consequences of using 8-bit coefficients and limiting the bit-
depth of the intermediate data to 16 bit is that all multiplications can be represented
with multipliers having 16 bits or less and that the accumulators before right shift
can be implemented with less than 32 bits for all transform stages.
Note also a relevant analysis in [
18
] that studies the dynamic range of the HEVC
inverse transform and provides additional information on the bit depth limits of the
intermediate data in the inverse transform.
6.2.6
HEVC Alternate 4
4 Transform
The alternate transform is applied to 4
4 Luma intra-prediction residual blocks.
The forward transform matrix is given by:
2
3
29
55
74 84
0
74
4
5
74
74
A
4
D
84
29
55
84
74 55
74
29
The inverse transform matrix is
A
4
.Elements
a
ij
of the alternate transform matrix
A
4
are a fixed point representation of Type-7 discrete sine transform (DST) obtained
as follows:
a
ij
D
round
128
2N
C
1
sin
.2i
C
1/ .j
C
1/
2
p
2N
C
1
The intermediate scaling and quantization/de-quantization used for the alternate
transform is the same as that for the core transform.
