Graphics Reference
In-Depth Information
2
4
3
5
d
16
d
16
d
16
d
16
d
16
d
16
d
16
d
16
d
4
d
12
d
20
d
28
d
28
d
20
d
12
d
4
d
8
d
24
d
24
d
8
d
8
d
24
d
24
d
8
d
12
d
28
d
4
d
20
d
20
d
4
d
28
d
12
D
8
D
(6.18)
d
16
d
16
d
16
d
16
d
16
d
16
d
16
d
16
d
20
d
4
d
28
d
12
d
12
d
28
d
4
d
20
d
24
d
8
d
8
d
24
d
24
d
8
d
8
d
24
d
28
d
20
d
12
d
4
d
4
d
12
d
20
d
28
Even-Odd
decomposition
for
the
8-point
inverse
transform
is
given
by
(
6.19
-
6.21
).
Even part:
2
3
2
3
2
3
z
0
z
1
z
2
z
3
d
16
d
8
d
16
d
24
x
0
x
2
x
4
x
6
4
5
4
5
4
5
d
16
d
24
d
16
d
8
D
(6.19)
d
16
d
24
d
16
d
16
d
8
d
16
d
24
d
8
Odd part:
2
4
3
5
2
4
3
5
2
4
3
5
z
4
z
5
z
6
z
7
d
28
d
20
d
12
d
4
d
28
d
12
x
1
x
3
x
5
x
7
d
20
d
4
D
(6.20)
d
12
d
28
d
4
d
12
d
4
d
20
d
20
d
28
Add/sub:
y
D
Œ
z
0
z
7
;
z
1
z
6
;
z
2
z
5
;
z
3
z
4
;
z
3
C
z
4
;
z
2
C
z
5
;
z
1
C
z
6
;
z
0
C
z
7
T
(6.21)
Note that the even part of the 8-point inverse transform is actually a 4-point
inverse transform (by comparing
6.19
with transpose of
D
4
in
6.11
) i.e.,
2
4
3
5
2
4
3
5
z
0
z
1
z
2
z
3
x
0
x
2
x
4
x
6
D
D
4
(6.22)
So the Even-Odd decomposition of the 4-point inverse transform (
6.14
-
6.16
) can
be used to further reduce computational complexity of the even part of the 8-point
transform in (
6.19
).
The direct 1D 8-point transform using (
6.17
) would require 64 multiplications
and 56 additions. The 2D transform will require 1,024 multiplications and 896
additions. An even-odd decomposition on the other hand requires 6 multiplications
for (
6.22
) and 16 multiplications for (
6.20
) resulting in a total of 22 multiplications.
It requires 8 additions for (
6.22
), 12 additions for (
6.20
) and 8 additions for
