% set time domain
T = (0:127)/128;
T = T';
A = Ncossinmat2(128);


% first signal pair
X = 2*cos(2*4*pi*T)-5*sin(2*10*pi*T);
Z = inv(A)*X;

figure(1)
subplot(2,1,1)
plot(T,X)
subplot(2,1,2)
plot(Z)

disp('Press a key');
pause


% second signal pair
X = 2*cos(2*4*pi*T)-5*sin(2*10*pi*T) + rand(128,1)-0.5;
Z = inv(A)*X;

figure(2)
subplot(2,1,1)
plot(T,X)
subplot(2,1,2)
plot(Z)

disp('Press a key');
pause

% third signal pair
% non integer frequency
X = 2*cos(2*10.2*pi*T);
Z = inv(A)*X;

figure(3)
subplot(2,1,1)
plot(T,X)
subplot(2,1,2)
plot(Z)

disp('Press a key');
pause


% fourth signal pair
% repeating pattern
X = zeros(128,1);
X(1:2:128) =1
Z = inv(A)*X;

figure(4)
subplot(2,1,1)
plot(T,X)
subplot(2,1,2)
plot(Z)

disp('Press a key');
pause

% fifth signal pair
% even signal
X = (0:63)/64;
X = [X';flipud(X')];
Z = inv(A)*X;

figure(5)
subplot(2,1,1)
plot(T,X)
subplot(2,1,2)
plot(Z)

disp('Press a key');
pause

% sixth signal pair
% odd signal
X = T.^3-T.^2-((1-T).^3-(1-T).^2);
Z = inv(A)*X;

figure(6)
subplot(2,1,1)
plot(T,X)
subplot(2,1,2)
plot(Z)

disp('Press a key');
pause