# Sampled offset voltage data and its uncertainty

In a measurement process sometimes contant voltage output of a for example force transducer is logged as offset as a bias to be subtracted later from the dynamic measurement. When the sensor is at rest, this offset is sampled at a specific sampling rate and specific duration.

If we have the sampled data in time series of this offset how can we calculate the uncertainty of the mean value of the offset?

I mean what is the uncertainty of the mean value of the offset due to random noise? Is it the standard deviation or standard error? I want to be able to say “This is the mean value of the offset with this standard uncertainty”

• it depends on the level and nature of the noise =TBD What is noise Vpp, frequency or BW if random, and number of samples? These determine the answer. Knowing the SNR , spectrum and filtering choices one can optimize this or state what it is then what it needs to be – Tony Stewart Sunnyskyguy EE75 Mar 3 '19 at 19:20

## 1 Answer

If we have the sampled data in time series of this offset how can we calculate the uncertainty of the mean value of the offset?

Assuming that the reading is equal to the offset plus Gaussian noise that is independent, sample to sample, then you would first calculate the standard deviation of the noise, then you would calculate the standard deviation of the error after averaging $$\n\$$ samples of data.

That's a big assumption.

I mean what is the uncertainty of the mean value of the offset due to random noise? Is it the standard deviation or standard error? I want to be able to say “This is the mean value of the offset with this standard uncertainty”

The mean value of the estimate of the offset, assuming the conditions set out above, is a homework problem for a basic statistics class. It's more or less (estimated standard deviation) / sqrt(n), where n is the number of samples.

• The various ways that an offset could diverge from the simplistic model above, and what to do about it, encompasses about half the field of metrology, and requires a fairly in-depth knowledge of the particular sensor you're using, the electronics you're doing the signal conditioning with, and the requirements of your measurement (because you don't want to over- or under-spend on your metrology equipment). You may well succeed with the assumption above -- but, maybe not. – TimWescott Mar 3 '19 at 19:39