Practically bandlimited signals do not occur in nature. That means neither waveforms nor realizable bandlimiting filters are strictly bandlimited. Thus, realizable bandlimited signals, always contain some aliasing.
These signals and filters can, however, be considered to be essentially bandlimited. By this, we mean that a bandwidth can be determined beyond which the spectral components are attenuated to a level that is considered negligible.
When a continuous-time band-limited signal is sampled at a rate lower than Nyquist rate fs < 2fm , then the successive cycles of the spectrum G(ω) of the sampled signal g(t) overlap with each other as shown in fig.1 .
Fig.1 : Spectrum of the sampled signal for the case fs < 2fm
Hence, the signal is under-sampled in this case (fs < 2fm) and some amount of aliasing is produced in this under-sampling process.
In fact, aliasing is the phenomenon in which a high frequency component in the frequency-spectrum of the signal takes identity of a lower-frequency component in the spectrum of the sampled signal.
From fig.1, it is clear that because of the overlap due to aliasing phenomenon, it is not possible to recover original signal x(t) from sampled signal g(t) by low-pass filtering since the spectral components in the overlap regions add and hence the signal is distorted.
Since any information signal contains a large number of frequencies, so, to decide a sampling frequency is always a problem.
Therefore, a signal is first passed through a low-pass filter. This low-pass filter blocks all the frequencies which are above fm Hz.
This process is known as band limiting of the original signal x(t).
This low-pass filter is called pre-alias filter because it is used to prevent aliasing effect.
After band-limiting, it becomes easy to decide sampling frequency since the maximum frequency is fixed at fm Hz.
Hence to avoid aliasing:
(i) Pre-alias filter must be used to limit band of frequencies of the signal to fm Hz.
(ii) Sampling frequency fs must be selected such that fs > 2fm