Graphics Reference
In-Depth Information
X
0
X
1
X
2
X
3
X
4
X
5
X
6
X
7
Fig. 10.11
Unified luma and chroma interpolation filters with inputs reordered. The coefficients
for x
3
(in
dashed box
) can be implemented with two adders and three multiplexers as shown in
Fig.
10.12
X
3
Fig. 10.12
Time-multiplexed Multiple Constant Multiplication for x
3
A reorder of the filter inputs is first applied to reduce complexity based on
symmetry as shown in Fig.
10.11
. Note that two sets of the chroma filter coefficients
are placed in x
1
and x
6
, instead of x
2
and x
5
, due to the similarity with the luma
coefficients 4 and 1. There are only seven cases left. The design principle adopted
here is to optimize TMMCM coefficients for each filter input. As an example, the
design for x
3
isshowninFig.
10.12
.
In the canonical signed digit representation, the coefficients have at most three
non-zero digits which determines the number of adders to be 2. The non-zero digits
are partitioned into three groups (n, m and r ) such that each group has at most
one non-zero digit. Finally, the three partitions are summed with partitions having
similar bitwidths added first.
Compared to algorithmically generated filter designs using [
15
], this design has
a 5-31 % lower area as shown in Table
10.7
.
Combining all the presented techniques, the complete 1-D filter is shown in
Fig.
10.13
using only 13 adders. Regarding the bitwidth increase between the input
and output, the case of luma 1/2-pel position gives the largest values for both
