Prefiltering to Avoid Aliasing In processing analog signals using discrete-time systems, it is generally desirable to
minimize the sampling rate. This is because the amount of arithmetic processing required
to implement the system is proportional to the number of samples to be processed.
If the input is not bandlimited or if the Nyquist frequency of the input is too high,
prefiltering maybe necessary. An example of such a situation occurs in processing speech
signals, where often only the low-frequency band up to about 3 to 4 kHz is required for
intelligibility, even though the speech signal may have significant frequency content in
the 4 kHz to 20 kHz range. Also, even if the signal is naturally bandlimited, wideband
additive noise may fill in the higher frequency range, and as a result of sampling, these
noise components would be aliased into the low-frequency band.
Could someone explain please the point below and why it is a problem?
Ie, why is it a problem if noise components are aliased into the low-frequency band?

&quot;Also, even if the signal is naturally bandlimited, wideband
additive noise may fill in the higher frequency range, and as a result of sampling, these
noise components would be aliased into the low-frequency band.&quot;
Let's look at a simple example: you have speech signal that has a sinusoidal noise component at 7 kHz.
If you sample this at 8 kHz without pre-filtering, the noise will alias down to 1kHz and contaminate your speech signal in a very important frequency region.
If you pre-filter at 4 kHz, the noise will be gone.