% This script demonstrates the effect of too small a time window on the 
% DFT of a signal that is a sum of sines.


% Interval end points
t_low = 0;
t_high = 1.25;
%t_high = 1;
%t_high = 2;
%t_high = 4;
%t_high = 8;

% Time step size
del_t = 0.01;
%del_t = 0.01;
%del_t = 0.02;
%del_t = 0.04;
%del_t = 0.08;

% Time Points
T = [t_low:del_t:t_high];

% Number of time points
N = length(T);

% Amplitudes and frequencies of components
a1 = 1;
w1 = 2*pi;
a2 = 1;
a2 = 0;
w2 = 1*pi;

% Construct signal
X = a1*sin(w1*T) + a2*sin(w2*T);

% Compute the DFT of the signal and the corresponding frequencies.
F = fft(X);
W = [0:N-1]*2*pi/(N*del_t);

% Plot results
figure(1);
plot(T,X);
figure(2);
plot(W,abs(F));