# Statistical noise measurement

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?

• I assume it's a kind of "root of the (mean minus datum)^2" summation thing... – user32885 Aug 11 '14 at 13:06
• 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
• 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. – user32885 Aug 11 '14 at 13:16
• 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
• Does the noise you see include ADC self-generated noise? – Andy aka Aug 11 '14 at 14:05

## 1 Answer

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: -

1. Subtract a sample value from the average
2. Square that new value
3. Sum all the squared values
4. Divide the total by the number of samples
5. 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.

• 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
• 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. – user32885 Aug 11 '14 at 14:22
• @sbell in my final paragraph I made an attempt to cover your concern. – Andy aka Aug 11 '14 at 14:24