CORDIC-based DDFS Architectures - Digital Design of Signal Processing Systems: A Practical Approach - page 490

S1 The algorithm then performs N iterations for i ¼ 1, ... , N 1, and performs the following set of

computations:

s 1 ¼ 1 when i > 0 else it is 1 ð 12 : 14a Þ

x i þ 1 ¼ x i s i 2 i y i ð 12 : 14b Þ

y i þ 1 ¼ s i 2 1

x i þ y i ð 12 : 14c Þ

i þ 1 ¼ i s i tan 1 2 i

ð 12 : 14d Þ

All the values for tan 1 2 i are pre-computed and stored in an array.
S2 The final iteration generates the desired results as:

cos d ¼ x N

sin d ¼ y N

The following MATLAB code implements the CORDIC algorithm:

% CORDIC implementation for generating sin and cos of desired angle
% theta_d
close all
clear all
clc
% theta resolution that determines number of rotations of CORDIC
% algorithm
N = 16;
% generating a tan table and value of constant k
tableArcTan = [];
k=1;
for i=1:N
k=k*sqrt(1+(2^(-2*i)));
tableArcTan = [tableArcTan atan(2^(-i))];

end

k = 1/k;
x = zeros(1,N+1);
y = zeros(1,N+1);
theta = zeros(1,N+1);

sine = [];
cosine = [];

% Specify all the values of theta
% Theta value must be within -0.9579 and 0.9579 radians

theta_s = -0.9;
theta_e = 0.9;
for theta_d = theta_s:.1:theta_e
% CORDIC algorithm starts here
theta(1) = theta_d;
x(1) = k;