CORDIC算法实现极坐标（polar）到直角坐标系(Cartesian)的变换。
1: function [horizonal,vertical]=polar2car(mag, pha);
2: x =mag;
3: y =0;
4: z=pha;
5: d=0;
6: i=0;
7: k = 0.6073; %K 增益
8: x = k*x;
9: while i<50
10: if z<0 d =-1;
11: else d = 1;
12: end
13: xNew=x-y*d*(2^(-i));
14: y=y+x*d*(2^(-i));
15: z=z-d*atan(1/2^(i));
16: i=i+1;
17:
18:
19: x=xNew;
20: end
21: horizonal = x;
22: vertical = y;
CORDIC算法实现直角坐标到极坐标系的变换。
1: function [mag, pha]= car2polar(x,y);
2:
3: %y =0;
4: %将直角坐标系中的点（x,y）旋转到x轴，旋转的角度即为其极坐标的相位，在x轴的长度等于极坐标的幅度
5: d=0; %可用于求相位，幅度
6: i=0;
7: z=0;
8: k = 0.6073; %K 增益
9:
10: while i<50
11: if y<0 d = 1;
12: else d = -1;
13: end
14: xNew=x-y*d*(2^(-i));
15: y=y+x*d*(2^(-i));
16: z=z-d*atan(1/2^(i));
17: i=i+1;
18:
19:
20: x=xNew;
21: end
22: x = x*k;
23: mag=x;
24: pha=z;
验证：
[a,b]= polar2car( 1,pi/3)
a =
0.5000
b =
0.8661
[a,b]= car2polar( 0.5000, 0.8661)
a =
1.0001
b =
1.0472
计算正切值atan只需将直角坐标变换为极坐标的程序中取出最后的角度值，即可得到反正切值。
1: function [ pha]= cordic_arcsin(c);
2:
3: %y =0;
4: %将点（1，0）旋转至其纵坐标=c,旋转的角度为角度 求反余弦也是同样道理
5: d=0;
6: i=0;
7: z=0;
8: x=1;
9: y=0;
10: k = 0.6073; %K 增益
11: xNew = x* k;
12: while i<100
13: if y<=c d = 1;
14: else d = -1;
15: end
16: x =xNew-y*d*(2^(-i));
17: y=y+xNew*d*(2^(-i));
18: z=z+d*atan(1/2^(i));
19: i=i+1;
20:
21:
22: xNew=x;
23: end
24:
25: %mag=x;
26: pha=z;
1: function [pha]= cordic_arccos(c);
2:
3: %y =0;
4: d=0;
5: i=0;
6: z=0;
7: x=1;
8: y=0;
9: k = 0.6073; %K 增益
10: xNew = x* k;
11: while i<100
12: if x>=c d = 1;
13: else d = -1;
14: end
15: x =xNew-y*d*(2^(-i));
16: y=y+xNew*d*(2^(-i));
17: z=z+d*atan(1/2^(i));
18: i=i+1;
19:
20:
21: xNew=x;
22: end
23:
24: %mag=x;
25: pha=z;
1: function [ pha]= cordic_arctan(x,y);
2:
3: %y =0;
4: %将点（x,y）旋转到x轴所需要的角度
5: d=0;
6: i=0;
7: z=0;
8: k = 0.6073; %K 增益
9: x = x*k;
10: while i<50
11: if y<0 d = 1;
12: else d = -1;
13: end
14: xNew=x-y*d*(2^(-i));
15: y=y+x*d*(2^(-i));
16: z=z-d*atan(1/2^(i));
17: i=i+1;
18:
19:
20: x=xNew;
21: end
22:
23: %mag=x;
24: pha=z;
1: function [sine,cosine] = cordic_sine(angle);
2: % Initialitation
3: %%angle=30 ;
4: x = 1;
5: y = 0;
6: z = angle;
7: d = 1;
8:
9: i = 0; % Iterative factor
10: k = 0.6073; %K Factor
11: xNew = k*x;
12: while i < 50
13: if z <=0 d =-1;
14: else d = 1;
15: end
16: x= xNew -d*y*2^(-i);
17: y=y+d*xNew*2^(-i);
18: z=z-d*atan(2^(-i));
19: i=i+1;
20: xNew=x;
21: end
22: cosine = x
23: sine = y