% EE 438 Digital Signal Processing with Applications - Spring 1997
% 2-D signals and systems
% 2-D cosine wave and spectrum 
% cos2d.m
%---------------------------------------------------------------
% Initialize
clear all;
close all;
%---------------------------------------------------------------
% Parameters
degrees = 30;	% "direction" of cosine
P = 16;		% period of cosine
M = 128;	% dimensions of image (MxM)
%---------------------------------------------------------------
%Initialize colormap
mcomp = 0 : 1.0 ./ 255 : 1.0; % output colors lie in [0,1]
map = [mcomp' mcomp' mcomp'];

index = (0:1:M-1);
x = ones(M,1)*index;
y = x(:,end:-1:1)';
theta = pi*degrees/180;
rho = 1/P;
u_0 = rho*cos(theta)
v_0 = rho*sin(theta)
g = 0.5 + 0.5*cos(2*pi*(u_0*x + v_0*y));
figure(1);
image(g*255);
colormap(map);
axis('off');
axis('image');
title('g(x,y)=0.5(1+cos(u_0x+v_0y))')

g = fftshift(g);
G = fft2(g);
G = fftshift(G);
Gmag = abs(G);
Gmax = max(max(Gmag));
figure(2);
image(Gmag*255/Gmax);
colormap(map);
axis('off');
axis('image');
title('log|G(u,v)|');