CORDIC原理与FPGA实现（2）

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