%Script file for "noisy circle"

t=linspace(0,100,1500);
X=[cos(t') sin(t') 0.1*randn(1500,1)];
Mix=randn(3,3);

Z=X*Mix;
Mix =[ -0.3560    0.7018   -1.2267
   -1.8924   -0.2936    3.0195
    0.4906   -0.5868    1.6093];

figure(1)
plot3(Z(:,1),Z(:,2),Z(:,3));

Z=Z-repmat(mean(Z),1500,1);  %Mean subtract

[U,S,V]=svd((1/1500)*Z'*Z);  %Covariance
Y=Z*U;  %This is the data in the PCA Coordinates

figure(2)
subplot(3,1,1)
plot(Y(:,1));
subplot(3,1,2)
plot(Y(:,2));
subplot(3,1,3)
plot(Y(:,3));

[U,V,P,C,S]=gsvd(Z,diff(Z),0);  %Clean signals in U
figure(3)
subplot(3,1,1)
plot(U(:,1));
subplot(3,1,2)
plot(U(:,2));
subplot(3,1,3)
plot(U(:,3));