Multiplier-less Multiplication by Constants - Digital Design of Signal Processing Systems: A Practical Approach - page 278

¼ 3 ¼ 1 þ 2 1 h 0

¼ 3 ¼ 2 2 h 0 1

¼ 53 ¼ 1 þ 13 2 2 h 1

¼ 2 4

13 3

¼ 53 ¼ 65 3 2 2 h 1

¼ 2 6 65 þ 1

h 1 ¼ 53 ¼ 56 3

¼ 2 6 2 3 56

¼ 585 ¼ 293 2 1 h 2 1

293 ¼ 2 8 þ 37

¼ 3 2 3 37 þ 13

2 3

h 2 ¼ 585 ¼ 65 þ 65

The graphical representations of these options are shown in Figure 6.13. Although there are
several other options for each coefficient, only a few are shown to demonstrate that generating all
these options and then finding the ones that maximize sharing of intermediate and final results is
complex. For this example, the best solution picks the first sub-graph for h 0 and second sub-graphs
for h 1 and h 2 . An optimized architecture that uses these options is shown in Figure 6.14.

1 1

3

3 13

1

<<1

+

- <<3

<<4

+

1

3

+

13

37

<<2

<<8

+

1

1 1

+

53

293

<<2

-

+ <<1

-

1 1

+

3

585

<<6

+

3

65

- <<2

65 65

+

<<3

53

+ 1 1

585

<<6 <<3

-

+

3

56

-

+
53

Figure 6.13 Decomposition of {3,53,585} in sub-graphs for maximum sharing