Sampling Theorem

SAMPLING:   A continuous time signal can be represented in its samples and can be recovered back when sampling frequency f_s is greater than or equal to the twice the highest frequency (fm) component of message signal. i. e  fs ≥ 2fm.

Consider a continuous time signal x(t). The spectrum of x(t) is a band limited to f_m Hz. Sampling of input signal x(t) can be obtained by multiplying x(t) with an impulse train δ(t) of period T_s. The output of multiplier is a discrete signal called sampled signal which is represented with y(t) in the following diagrams:

ALIASING:

Different signals to become indistinguishable (or aliases of one another) when sampled is called Aliasing. Aliasing occurs when a system is measured at an insufficient sampling rate.

 Reference:

http://www.tutorialspoint.com/signals_and_systems/signals_sampling_theorem.htm