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Usually it's completely sufficient to take 10 .. 16 samples to get a good estimate for the quantity to be measured, and also that implies that the StD is sufficiently 'stable'.
Taking more samples to 'improve' the StD is counter productive, as you will get instabilities of higher order into your measurements, e.g. mid- and long term drifts.
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As you cite my measurements, I just want to refer to the Allan Deviation method, where you get a good picture of instabilities or noise over different timescales.
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If the noise is just white noise, relatively short sets of readings give good estimates for the standard deviation. However if there is some extra 1/f or popcorn noise or drift or a other superimposed signal the RMS calculation can fluctuate and different lengths may show different values. In this case the Allan deviation plot may be more helpful than just the standard deviation. A single number is just not sufficient to characterize complex noise.
So I would interpret the fluctuations seen in the stD calculated over 100 samples each as an indication that there is not just white noise.
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RMS noise and StD share basically the same formula, so under some precautions, like observation of the different noise sources, the StD gives a good estimate for the noise figures, as I have demonstrated with my diagram for apertures ranging from 1.4µs to NPLC of 1000.
I can't observe, that there is a large spread, compared to the hp specification, and also within the whole graph.
Please also take notice, that such measurements are always plotted on a logarithmic scale, so small variations do not play a role.
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For comparison, the dataset was filled with pure white noise (16154 samples, SD 100nV, mean 1.53µV - same as original Data).
With several runs with different white noise sets I get (limited represantative):
| rolling SD(10) | rolling SD(100) | rolling SD(1000) | SD(16154) |
multiple runs white noise | ~+-50...100% | ~+-20...30% | ~+-5...10% | 100nV <+-1% |
original dataset | -72% +80% | -26% +26% | -7% +13% | 100nV |
An Example with white noise is attached.
The spreading of rolling ACRMS/SD over white noise for short sets with 10 samples are in the range of ~0...200nV.
In the context of comparison I would not call that good estimates for given ACRMS/SD of 100nV over all samples.
If this is my misconception of statistical methods
for this purpose: I can suffer, so slap me hard on the head
In contradiction for large sets the ACRMS/SD may be dominated by other noise sources, as you already stated.
I am wondering if it would be appropriate to use rolling ACRMS/SD with short sets on a large dataset and take e.g. the Mean of all rolling ACRMS/SD?
Intention is to have a high-pass filter to get rid of probably dominant LF Noise Sources (Drift, TC, popcorn-noise?) whilst maintaining good approximation of the remaining mostly white noise part.
Clearly there is not one number to deal with "complex" noise, but if it is possible to separate appropriate into a couple of numbers for different noise types and other influences, this would have value.
The shorted DMM seems to have mostly white noise, but you are right, for deeper insight the Allan deviation would be helpful.
We want to compare the ACRMS/SD of shorts for different DMMs at given PLC and range.
Who is 'WE'? Plural Majestic?
'WE' meant in the sense the participants in "DMM Noise comparison testing project"
I am pretty shure you got the point