# Are there any advantages oversampling?

Are there any advantages of undersampling or oversampling in signal processing point of view?

• What do you mean by "Nyquist"? – MBaz Jul 15 '20 at 17:33
• Then, I don't understand your question. Do you mean advantages of sampling at the Nyquist frequency, compared to sampling below it, and above it? – MBaz Jul 15 '20 at 18:20
• We keep asking for clarity, and you keep repeating what you've already said. It's not even clear if you mean to ask if the Nyquist sampling theorem is of use for analysis, or if it's somehow of use directly. Please edit your question to give us a concrete example of something you're contemplating doing, and how you see using "Nyquist" in this context. Then we can help. – TimWescott Jul 15 '20 at 19:23
• Yes. I can read, thank you. And I can think. And I've got 30 years experience in industry applying DSP principles. And your question, as written, makes no sense. So don't waste any more time just repeating it, with or without shouting. Help us help you, and we will help you. Or don't -- that's your choice. – TimWescott Jul 15 '20 at 19:32
• It seems you understanding of Nyquist is the problem here. First of all, Harry Nyquist was american physicist who discovered/invented a many different things. I assume you are referring to the Nqyuist-Shannon Sample Theorem in which the Nyquist frequency plays a dominant role. .They are both a fundamental properties of discrete signals and systems. They don't have advantages or disadvantages they just are. You can't work around or ignore them. – Hilmar Jul 15 '20 at 19:35

## 2 Answers

1. Nyqusit Frequency simply means "half the sample rate"
2. Undersampling means your signal bandwidth is higher than the Nyquist Frequency. You get aliasing
3. Oversampling means your signal bandwidth is lower than the Nyquist Frequency. You don't get aliasing
4. Most practical applications choose a Nyquist Frequency that's slightly higher than the highest frequency of interest. That gives some space to manage the transition band between the signal frequencies and the Nyqusit Frequency (at which the signal should be 0). For example audio is considered to have 20 kHz bandwidth but the typical Nyquist frequencies are 22.05 kHz or 24 kHz

Let me suppose that by Nyquist, you mean that there is some frequency $$F_s$$ such that there is a existence theorem that says:

if one samples any continuous $$s(t)$$ at $$F_s$$ (or above), $$F_s$$ denoting an extremal frequency or a extremal bandwidth, to get a discrete signal $$s[k]$$, then one can recover $$s(t)$$ by some algorithm.

• Case 0: neither oversampling nor undersampling, you sample at $$F=F_s$$. Theoretically you are safe, but sampling systems are never perfect (noise, quantization, jitter, lag, limited time), and reconstruction algorithms not often stable, so there is a risk that some of the signals you sample, you lose information (like with aliasing)
• Case 1: oversampling , you sample at $$F>F_s$$. Theoretically you are safer, and many systems specify that 10% or 20% above $$F_s$$ are safe bets for relatively clean signals. Higher, you can hope to have more chance to retrieve weak signals in noise, etc. but the higher the rate, the larger the signal to store and manipulate, and, sometimes, (potentially ) better is worse.
• Case 2: undersampling , you sample at $$F. Theoretically you will lose information. But if the signals you are interested in are not "all potential signals" satisfying the limits, but a restricted set, or if the processing you do is robust, or the features you extract are not so demanding, then with high probably, you will get what you want at a cheaper price.