Digital Signal Processing Reference
In-Depth Information
cos(
θ
d
) using Modified CORDIC
sin(
θ
d
) using Modified CORDIC
Modified CORDIC
cos(
Modified CORDIC
sin(
θ
)
θ
)
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
0.5
1
1.5
0
0.5
1
1.5
θ
d
in radian
θ
d
in radian
Figure 12.15
Results using CORDIC and modified CORDIC algorithms
Figure 12.15 shows the results of using CORDIC and modified CORDIC algorithms. A mean
squared error (MSE) comparison of the two algorithms for different numbers of rotations N is given
in Figure 12.16. The error is calculated for P sets of computation by computing the mean squared
difference between the value cos
i
in double-precision arithmetic and the value using the CORDIC
algorithm for the quantizing value of
1) format. The expression for MSE while
considering
i
as an N-bit number in Q1.(N
1) format is:
i
as
Qi
in Q1.(N
P
1
1
P
2
where
Qi
¼
round
ð
i
2
N
1
ð
cos
i
CORDIC
Q
ðÞ
Þ
MSE
N
¼
Þ
i¼
0
It is clear from the two plots that, for N
>
10, mean squared error for both the algorithm is very
small, so N
¼
16 is a good choice for the CORDIC algorithms.
12.5 Hardware Mapping of Modified CORDIC Algorithm
12.5.1 Introduction
One issue in a modified CORDIC algorithm is eliminating tan 2
i
from (12.17) as it requires
multiplication in every stage. This multiplication can be avoided for stages for i
>
4 as the values of
tan 2
i
can be approximated as:
tan 2
i
2
i
for
i >
4
ð
12
:
18
Þ
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