function aliasDemo(n, max_x = 1, freq=10)
  x = max_x*(0:n-1)/n;
  f_of_x = @(t, fr) cos(2*pi*fr*t);
  y = f_of_x(x, freq);
  xs = 0:max_x/1000:max_x;
  ys = f_of_x(xs, freq);
  figure(1)
  plot(x, y, 'b*', xs, ys, 'b-', 'markersize', 4, 'linewidth', 2)

  Y = fft(y);
  f = (0:n/2)/max_x;
  pow = abs(Y(1:n/2+1));
  fndFreq = find(pow == max(pow));
  figure(2)
  plot([f;f], [0*pow;pow], 'r-', f,pow,'b*', 'linewidth',2, 'markersize',4)
  axis([-1 max(f)+1 0 pow(fndFreq)+1])

  pause
  figure(1)
  hold on
  plot(xs, cos(2*pi*f(fndFreq)*xs), 'r-', 'linewidth', 2)
  hold off
end