Sampling

A band limited signal $s(t)$ with bandwidth $\Delta \nu$ can be uniquely represented by a time series obtained by periodically sampling $s(t)$ at a frequency $f_s$ (the sampling frequency) which is greater than a critical frequency $2\Delta\nu$ (Shannon 1949). The signal is said to be `Nyquist sampled' if the sampling frequency is exactly equal to the critical frequency $2\Delta\nu$.

The spectrum of signals sampled at a frequency $<$ 2 $\Delta \nu$ (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.