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Aliasing
Aliasing is the effect that results when a signal is sampled at too slow a rate. When this occurs the signal may not be able to be reproduced accurately.
How do we define a rate that is too slow?
The minimum sampling rate that we must use to guarantee no aliasing of a signal is called the Nyquist Rate. To define the Nyquist Rate, we establish the sampling time as:
$ T=\ \frac{2\pi}{\omega_s},\, $
where $ \omega_s $ is the sampling frequency.
As a rule, we know that $ \omega_s > 2\omega_m $, where $ 2\omega_m $ is the Nyquist Rate, so we see that if we want a recreated signal with NO aliasing, our sampling frequency must be greater than the Nyquist Rate. To be clear, it should be noted that $ \omega_m $ is the maximum frequency of the given band-limited signal.
How to Avoid Aliasing
Now that we know what aliasing is, we know how to use it to avoid the effect of aliasing. To avoid aliasing in sampling a signal, just make sure your sampling rate is greater than the Nyquist Rate.
The Problem With Aliasing
The problem that results if a signal is sampled at a rate equal to or less than the Nyquist Rate is an inaccurately reproduced signal. It may result in anything from very slight defects in an audio signal to total noise and nothing close to the original signal.
