Aliasing

Alaising is what occurs when you sample the highest frequency component of a signal less than two times and then are not able to reconstruct the original signal from the sampled data. This is generalized by Nyquists sampling theorem that says the signal must be sampled at a frequency of 1/T > 2*fmax. In the example shown below a wave has a sample period of T and thus a sampling frequency of 1/T. fmax in this case is greater than 1/2T so there is some overlap in the bandwidth. This overlap of X(f) will add constructively in the sampled signal. Now when we wish to convert this sampled signal back to the the original we can not because we have no idea what it orginally looked like, or what frequency components it had.