% ftfft script approximates Fourier transform
% of x(t) based on samples x(t1),...,x(t2),
% where samples are uniformly spaced by 1/fs.

% EXAMPLE:  x(t) = cos(2*pi*10*t)

subplot(2,1,1)             % Plot waveform x(t)
t = linspace(0,1,200);
plot(t,cos(2*pi*10*t))
title('\itx\rm(\itt\rm)=cos(2*pi*10*\itt\rm)')
grid on

fs = 24; % Select sampling rate.  Since the cutoff freq. is 10,
         % the Nyquist rate is 20.

t1 = 0;                  % Sample x(t) for t1<=t<=t2 ...
t2 = 4;
n1 = ceil(fs*t1);        % ... using time values of the form n/fs
n2 = floor(fs*t2);
nvec = [n1:n2];
t = nvec/fs;             % Note that we are redefining t

x = cos(2*pi*10*t);      % Compute function values

[y,f] = dtftfft(x,n1,0); % Compute DTFT on [-1/2,1/2]
f = f*fs;                % Convert freq. to [-fs/2,fs/2]
y = y/fs;                % Scale DTFT

subplot(2,1,2)
plot(f,abs(y))
title('Approximate Fourier transform')
grid on