You are correct Pierre, I was totally off. 

From a fourier series prospective, if the data are filtered, i.e. approximated by the summation of a fewer number of sinusoids, then the summation of these signals, should only contain those sinusoids.  So the summation of several band-limited signals should still be band limited.  

Again, I apologize, I was being stupid, and should have just looked at my scripts ... which I am doing now :)

-cc