fun = @(x) max(0,1-abs(x-pi)/2); 
  fun = @(x) exp(sin(x));

  N = 24; 
  h = 2*pi/N; 
  x = h*(0:N-1)';
  v = fun(x);

  v_hat = fft(v);
  k = [0:N/2, -N/2+1:-1];

  ng = 100;
  xg = linspace(0,2*pi,ng);
  fg = exp(1i*xg'*k) * v_hat / N;
  fg = real(fg);
  plot(x,v,'o',xg,fg,'-')