**1 Answer**

written 2.6 years ago by |

The overall conditions for the efficient sampling of a signal and its reconstruction is given by sampling theorem.

A band limited signal of finite energy which has no frequency components higher then w hertz, is completely described by specifying the values of the signal at instants of time separated by $(\frac{1}{2w})$ seconds.

A band width signal of finite, energy, which has no frequency components higher than w hertz,be completely recovered from a knowledge of its samples taken at the rate of 2w per second.

The sampling rate of 2w samples per second for a signal bandwidth of q, is after called the Nyquist rate.

**Aliasing:** To preserve all information in the unsampled signal, we must ensure that the spectrum "islands" do not overlap when replicating the spectrum, if they overlap, we can no longer extract the original signal from the samples this overlapping is known as "Aliasing"

Aliasing allows higher frequencies to disguise themselves as lower frequencies.

To avoid aliasing, you must preserve the following condition.

$\frac{1}{T} \geq 2 BW$

This result can be expressed in terms of sampling frequency as

F sampling (Fs) = 2BW

Thus minimum sampling frequency necessary for sampling without aliasing is 2 BW this result is generally known as Nyquist criterion.