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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?

"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."

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    $\begingroup$ well, whether it's signal, interference, or noise, folding it back into the baseband increases the noise or interference in the baseband. so why wouldn't you want it removed before it gets added to the baseband because of aliasing in the down-sampling. don't you want that undesired out-of-baseband stuff gone before it get's added? it's hard to un-add it after the fact. $\endgroup$ – robert bristow-johnson Dec 20 '20 at 7:01
  • $\begingroup$ @DSPinfinity: You could edit your question to address any remaining doubts after having read and understood Robert's comment. It's simple: aliasing is (usually) bad, no matter what is aliased. $\endgroup$ – Matt L. Dec 20 '20 at 11:29
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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.

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  • $\begingroup$ Could you please explain also "If you sample this at 8 kHz without pre-filtering, the noise will alias down to 1kHz "1? $\endgroup$ – DSPinfinity Dec 20 '20 at 18:15
  • $\begingroup$ @DSPinfinity: do you know what aliasing is and how it works? If you sample a 7 kHz sine wave with a sample rate of 8 kHz, the result is the same as sampling a 1kHz sine wave, so it's indistinguishable from a 1 kHz sine wave. $\endgroup$ – Hilmar Dec 21 '20 at 20:19

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