%
%  SDSMT Signals Class EE312
%  Dr. Charles R. Tolle
%
%  The use of the FFT and an example of aliasing.
%
Ts = .1;                                % sampling time
Fs = 1 / Ts;                            % sampling frequency
S  = 256;                               % number of samples

t = 0:Ts:(S-1)*Ts;                      % time signal
x = cos(2*pi*t);                        % x(t) signal of interest


f = linspace(0,Fs,S);                   % define the fft frequencies
aX = abs(fft(x));                       % calculate the magnitude protion 
                                        % of the FFT(x(t))
pX = angle(fft(x));                     % calculate the angle protion 
                                        % of the FFT(x(t))

% plot x(t)
figure(1),subplot(3,1,1),plot(t,x)
figure(1),subplot(3,1,1),title('x(t)= cos(2 \pi t)') 

% plot the resultant mag and angle of the fft from 0-Fs
figure(1),subplot(3,2,3),plot(f,aX)     
figure(1),subplot(3,2,3),title('|fft(x(t))|') 
figure(1),subplot(3,2,5),plot(f,pX)
figure(1),subplot(3,2,5),title('phase(fft(x(t)))') 

% plot the spectrum from -Fs/2 to Fs/2
figure(1),subplot(3,2,4),plot(f(1:S/2),aX(1:S/2),(f(1:S/2)-(Fs/2)),aX(((S/2)+1):S))
figure(1),subplot(3,2,4),title('|fft(x(t))| plotted from -Fs to Fs') 
figure(1),subplot(3,2,6),plot(f(1:S/2),pX(1:S/2),(f(1:S/2)-(Fs/2)),pX(((S/2)+1):S))
figure(1),subplot(3,2,6),title('phase(fft(x(t))) plotted from -Fs to Fs') 

for j= 1:Fs,
    if (j > Fs / 2)
        alias = 'Aliased ';
    else
        alias = '';
    end
    
    dt = 0:Ts/2:(S-1)*Ts;                 % double sample time signal
    dx = cos(2*pi*dt) + cos(2*pi*j*dt);     % x(t) signal double sample time
    x = cos(2*pi*t) + cos(2*pi*j*t);        % x(t) signal sampled

    aX = abs(fft(x));                       % calculate the magnitude protion 
                                            % of the FFT(x(t))
    pX = angle(fft(x));                     % calculate the angle protion 

    % plot x(t)
    figure(2),subplot(4,1,1),plot(t,x)
    figure(2),subplot(4,1,1),title([alias 'x(t)= cos(2 \pi t) + cos(2 \pi' ,num2str(j) ' t) sampled at: ' num2str(Ts)]) 

    % plot dx(t)
    figure(2),subplot(4,1,2),plot(dt,dx)
    figure(2),subplot(4,1,2),title(['x(t)= cos(2 \pi t) + cos(2 \pi' ,num2str(j) ' t) sampled at: ' num2str(Ts/2)]) 
    
    % plot the resultant mag and angle of the fft from 0-Fs
    figure(2),subplot(4,2,5),plot(f,aX)     
    figure(2),subplot(4,2,5),title([alias '|fft(x(t))|']) 
    figure(2),subplot(4,2,7),plot(f,pX)
    figure(2),subplot(4,2,7),title([alias 'phase(fft(x(t)))']) 

    % plot the spectrum from -Fs/2 to Fs/2
    figure(2),subplot(4,2,6),plot(f(1:S/2),aX(1:S/2),(f(1:S/2)-(Fs/2)),aX(((S/2)+1):S))
    figure(2),subplot(4,2,6),title([ alias '|fft(x(t))| plotted from -Fs to Fs']) 
    figure(2),subplot(4,2,8),plot(f(1:S/2),pX(1:S/2),(f(1:S/2)-(Fs/2)),pX(((S/2)+1):S))
    figure(2),subplot(4,2,8),title([alias 'phase(fft(x(t))) plotted from -Fs to Fs']) 

    pause(1)
end