A band limited signal with bandwidth can be uniquely represented by a time series obtained by periodically sampling at a frequency (the sampling frequency) which is greater than a critical frequency (Shannon 1949). The signal is said to be `Nyquist sampled' if the sampling frequency is exactly equal to the critical frequency .
The spectrum of signals sampled at a frequency 2 (i.e. under sampled) is distorted. Therefore the time series thus obtained is not a true representation of the band limited signal. The spectral distortion caused by under sampling is called aliasing.