> Averaging is not reducing the noise. Average is just the equivalent
> of an analogic integrator. And no, the analogic integrator is not
> "reducing" the noise. It just integrating it in the result (with other
> words is fooling you that there isn't there anymore based on the
> theoretical ideea that noise averaging is always zero - which is not
> entirely true, sampling time being essential for many types of noise)

You'd need to know the quailty of the noise before you could say
averaging was not effective. For example, the bandwidth / amplitude
of the noise compared with the signal being measured. Averaging a
digital noise isn't necessarily the same as integrating (eg RC) analogue
noise. You have the option of a majority decision and rejection, or
pattern matching to determine if a noise is out of character

I agree that s/w filtering is not the ideal way to clean up h/w noise,
but could compensate for it. For example if you know that noise is
typically 1 LSb and random, then it should "average out" to 1/2 LSb.
Techniques such as using jitter, adding random noise and statistics
could make for more meaningful results in some situations

But IANA maths or signal processing expert

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