Is there an accepted measure of noise in a data set? I am taking a series of reading from an ADC, which follow a trend (they are not random data points). However, they generally lie above and below the averaged value (running average, FIR low pass effectively). How do I get a measure of how much noise there is over a given interval?
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I assume it's a kind of "root of the (mean minus datum)^2" summation thing... – Aug 11 '14 at 13:06
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What are you doing? are you trying to study the ADC for noise or are you using the ADC to study a waveform? If the later what are the characteristics of he waveform? – placeholder Aug 11 '14 at 13:13
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The data is effectively one sample per second and I am collecting a trend line over minutes/hours. Most of the noise really is noise ie random fluctuations in what should be a smooth straight line. However, there is in the longer term a smooth variation in that straight line, for example a slow sine wave that corresponds to changes in ambient temp (a measurement artefact created by temperature dependent components and ideally absent in a strictly controlled enclosure). I want to know how to characterize the noise. – Aug 11 '14 at 13:16
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Why do you want to characterize the noise? There are a lot of ways to do it, but unless you give us some kind of goal, there's no basis to pick one. – Phil Frost Aug 11 '14 at 13:56
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Does the noise you see include ADC self-generated noise? – Andy aka Aug 11 '14 at 14:05
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The noise comes from a variety of sources - thermal, PID loop resonance, seismic... I need to characterize the noise in order to determine acceptable limits for manufacturing testing. Currently doing it manually ie "It looks like xxx mV on average" – Aug 11 '14 at 14:21
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If you have the average value of the data set you are interested in and all you want to compute is standard deviation (or RMS because it is the same) then: -
- Subtract a sample value from the average
- Square that new value
- Sum all the squared values
- Divide the total by the number of samples
- Take the square root
If the noise is small and might contain quantization noise then you are going to be less accurate with the noise value computed.
If the mean/average is expected to drift in time then you may choose to use a rolling average calculation so that a significant emerging offset does not make the noise value bigger than it actually is.

Andy aka
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Just a note: this will only give an accurate representation of the noise if the non-noise part of the signal is effectivly DC for the range of the moving average window – sbell Aug 11 '14 at 14:20
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I think it is about the best I am going to get for the time being. I just want something a bit more objective than looking at a graph and making a guess. – Aug 11 '14 at 14:22
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@sbell in my final paragraph I made an attempt to cover your concern. – Andy aka Aug 11 '14 at 14:24
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Please define "all" in the sentence "Sum all the squared values". Do you square all the values that make up the average as well? – Eugene Roche Nov 03 '21 at 01:24