41
Graph 2 - a plot of y sequence values against k
2.4
2
1.6
1.2
0.8
0.4
0
-0.4
-0.8
0
5
10 15 20 25 30 35 40 45 50
k
It is not surprising that the y values have been driven to zero since
. Furthermore it can be shown that
δ
−=
sgn(
)
y
k
k
n
∑ + = δ
−
k
, 2
y
y
x
+
1
0
0
n
k
=
0
k
n
∑
−
k
−=
δ
. 2
z
+
1
n
k
=
0
k
Thus,
x y
1 + + + = n n z x y . 1
0
0
0
x y
x y
y
+
0
1
0
n
≈
= − and hence
It follows that
, since the
n y values
z
z
+
+
1
1
n
n
x
0
0
0
are driven to zero for sufficiently large n.
The more interested reader should read the paper by Edwards and Underwood [2] for a more detailed analysis on the convergence of the CORDIC method for more complicated functions.
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