Image Processing Reference
In-Depth Information
XZ

2(2
2
n
2
n

1)2
2
n
3
(
x Z
)
 
x
2(
2
n
Y
 
2
2
n
TT
)
(66)
4
1
21
n
2
1
Where
Tvvv

(67)
5
6
7 2
21
n
1
vx


xx x
0
(68)
5
1,2
n
2
1,1
1,0
1,2
n
1
21
n
vY


YY
0
(69)
6
2
n
1
1
0
2
n
vx


xxxx
(70)
7
4,2
n
2
4,1
4,0
4,2
n
4,2
n
1
21
n
The hardware implementation of this converter relies on two modulo adders for realization
of (61) and (67). In other words, (61) needed two 2 n -bit CSAs with EAC and a 2 n -bit CPA
with EAC, and a (2 n +1)-bit CPA with EAC is used to realize (67). Besides, (66) only requires
one (4 n +1)-bit regular binary adder; the required multiplications all can be done using shift
and concatenation. The converter has been depicted in Fig. 4.
7. Complexity comparison
Table 1 presents the total hardware requirements and conversion delays of the reverse
converters for the large dynamic range four-moduli sets in terms of logic gates and FAs.
Note that A FA and D FA indicate the area and delay of one FA, respectively. It can be seen that
the fastest converter is the converter for moduli set {2 n -1, 2 n +1, 2 2n , 2 2n +1}. Because, the
dynamic range of this set is 6 n -bit while the dynamic range of moduli set {2 n -1, 2 n , 2 n +1,
2 2n +1} is 5 n -bit. Therefore, for providing the same dynamic range, the value of n for the first
Moduli set
Hardware Requirements
Conversion Delay
(8 n +2)A FA + ( n -1)A XOR + ( n -1)A AND
+ (4 n +1)A XNOR +(4 n +1)A OR
+ (7 n +1)A NOT + ( n )A MUX2×1
{2 n -1, 2 n , 2 n +1, 2 2 n +1 -1}
(12 n +5) D FA +3 D NOT + D MUX
(10 n +3)A FA + ( n +1)A XOR
+ ( n +1)A AND + (3 n -1)A XNOR
+( 3n -1)A OR + (7 n +3)A NOT
{2 n -1, 2 n +1, 2 2n , 2 2n +1 -1}
(12 n +6) D FA +2 D NOT
(11 n +6)A FA + (2 n -1)A XOR
+ (2 n -1)A AND + (4 n )A XNOR
+(4 n )A OR + (5 n +3)A NOT
{2 n -1,2 n , 2 n +1, 2 2 n +1}
(8 n +3) D FA + D NOT
(10 n +6)A FA + (4 n -3)A XOR
+ (4 n -3)A AND + (2 n -3)A XNOR
+(2 n -3)A OR + (6 n +3)A NOT
{2 n -1, 2 n +1, 2 2 n , 2 2 n +1}
(8 n +3) D FA + D NOT
Table 1. Hardware requirements and conversion delays of the reverse converters for the
large dynamic range four-moduli sets
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