# Oversampling a signal

I’ve built a circuit with an analogue sensor (70 Hz bandwidth) connected to a 24 bit ADC, which is oversampling the signal at 10 kHz. Nyquist sampling theorem implies I should sample by at least 140 Hz to reconstruct the signal.

Currently (if I’ve understood oversampling correctly) I’m oversampling by a factor of $$N = \frac{10000-140}{140} = 70$$. As the minimum sampling frequency is the Nyquist rate, and oversampling is a factor $$N$$ times this minimum rate. My questions are:

• Does this oversampling only reduce the noise introduced from the output of the analogue sensor (given the low bandwidth of the sensor) to the end of the ADC process?
• How much can I reduce the oversampling (which introduces a processor overhead) by for a negligible increase in the amount of noise to the signal?
• Could I do anything else to reduce the amount of oversampling, e.g increase the ADC resolution?

From that same page you link to:

A signal is said to be oversampled by a factor of N if it is sampled at N times the Nyquist rate.

So, you're sampling at $$1\cdot10^4\,\text{Hz}$$, that's $$N=\frac{10^4}{140}\approx 71$$; no need to subtract anything.

Does this oversampling only reduce the noise introduced from the output of the analogue sensor (given the low bandwidth of the sensor) to the end of the ADC process?

Oversampling alone doesn't reduce noise. It's what you do afterwards with the signal. Oversampling can be necessary to e.g. to be able to filter out the noise that can be shaped to your advantage.

How much can I reduce the oversampling (which introduces a processor overhead) by for a negligible increase in the amount of noise to the signal?

You need to define "negligible"; also, you need to think about the noise is distributed in frequency domain during your sampling process; there's no general answer.

Could I do anything else to reduce the amount of oversampling, e.g increase the ADC resolution?

I'm confused: The only way to reduce oversampling is to reduce the sampling rate.

Maybe you mean

to reduce the necessary amount of oversampling

Well, that fully depends on your signal, and what you want to do with it, and you forgot to tell us about either!

• Thanks for your reply! The sampling rate at 10K is the total sampling rate I’m reading the ADC, my rationale for subtracting the nyquist rate from it was that if N is the over sample rate then I would have thought that N = 0 would imply no oversampling i.e. only sampling at 140Hz. But I could be wrong! You’re right I missed it from my original question that I’m oversampling and then averaging (mean) the data to reduce noise - with this in mind does my original question make more sense? Also I was hoping to reduce the necessary oversampling so there is max increase of 2% noise on the signal.
– Joe
Jun 7, 2020 at 10:56
• yes, you're wrong; it's a factor, not an additional factor, so the definition of the wikipedia article is clear. But that really doesn't matter much here, does it? I Jun 7, 2020 at 11:07
• I'm still confused what you mean with "reduce oversampling", could you elaborate? Jun 7, 2020 at 11:08
• So if I made the assumption that at N = 71 the noise equalled 0 how much could I reduced the oversampling too e.g N = 65, for the noise to increase by 2%?
– Joe
Jun 7, 2020 at 11:12
• Also given I’m oversampling and averaging a much lower bandwidth signal is this going to reduce noise introduced from the sensor and ADC or is it just going to reduce noise from the ADC?
– Joe
Jun 7, 2020 at 11:24