Image Processing Reference
In-Depth Information
After a scaling according to (15) we can introduce the new set of variables for the 3 rd pipeline
stage:
4 X 0
11
1
1 C 0
4 2 S 2 X 4
1
C 3
C 2
+
S 4
S 4
=
=
(28)
X 8
S 6 X 12
C 1
1
S 4
S 4
C 7
S 2 C 4
S 6 C 4
S 4 C 5
S 2 C 6
S 6 C 6
=
=
S 1 X 2
S 7 X 14
S 3 X 6
S 5 X 10
1
S 4
S 2
S 6
C 7
C 5
C 6
C 4
101110
1
4 2
1
S 4
S 6
S 2
10
101
(29)
1
S 4
S 6
S 2
110
10
1
1
S 4
S 2
S 6
10
11
10
C 0,1 =
B 0,1 +
B 3,2
C 3,2 =
B 0,1
B 3,2
C 4,5,6 =
B 4,5,6 +
B 5,6,7
C 7 =
B 7
(30)
Let us notice that the structure of the right vector in (29) is exactly the same as in (22), but the
structures of the 6x4 matrices are different. In (22) the matrix comes from a transformation for
the odd indices supported by (21), while in (29) the matrix comes from a transformation of
even indices.
Scaled coefficients corresponding to odd indices
4 2 X k cos k
32
Z k
=
(31)
can be expressed by variables (25) and scaling factors (21) as follows:
=
±
Z 1,15
Z 3,13
Z 5,11
Z 7,9
1
S 4
S 2
S 6
B 15
B 11
B 13
B 9
S 1
S 3
S 5
S 7
B 14
B 12
B 10
B 8
1
S 4
S 6
S 2
S 3
S 7
S 1
S 5
(32)
1
S 4
S 6
S 2
S 5
S 1
S 7
S 3
1
S 4
S 2
S 6
S 7
S 5
S 3
S 1
Matrix (32) can be factorized as follows:
=
±
1
2 S 1 000
0 2 S 3 00
00 2 S 5 0
000 2 S 7
Z 1,15
Z 7,9
Z 5,11
Z 3,13
C 13 +
C 9 )
(
C 15 +
C 11 )+(
1
S 4
S 2
S 6
C 14
C 10
C 12
C 8
C 13 +
C 9 )
(
C 15 +
C 11 ) (
1
S 4
S 6
S 2
C 13
C 9 )
(
) (
1
S 4
S 6
S 2
C 15
C 11
C 13
C 9 )
(
)+(
1
S 4
S 2
S 6
C 15
C 11
(33)
where:
C 2,6
9,13
=
+
=
=
=
C 8,10,12
B 8,10,12
B 10,12,14
C 14,15
B 14,15
B 9,13 S 2,6
C 11
B 11 S 4
(34)
In the 4th pipeline step directly from (32) we can introduce new variables:
C 13 +
C 9
C 13
C 9
=
±
=
=
D 15,11
C 15
C 11
D 13
D 9
(35)
The rest of variables require 10 next multipliers, 3 adders/sub-tractors and 3 shift registers:
D 2,6
4,6,8,12
D 5,10 =
S 4 C 5,10
=
S 2,6 C 4,6,8,12
D 3.7.14 =
C 3,7,14
Search WWH ::




Custom Search