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Sensing Systems and Signal Processing
Dr Richard
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Reducing noise
Averaging Noise
If our signal repeats we can also average our signal to improve the SNR.
Why does it improve?
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Averaging Noise
S is a sample of the signal, n1 is a sample of the noise n.
The noise n has zero mean and standard deviation σ and is normally distributed (white noise)
S is not changing for repeated samples at the same time.
The mean of the final noise is the sum of the noise means and the variance of the final noise () is the sum of the variance associated with each noise samples.
The variance of the noise sample to sample is the same and the noise means are also zero.
We get the result that the noise reduces by the square root of the number of averages used.
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Just a few averages can have a big impact on the visibility of the signal.
Going from single shot (1) where the signal is hard to observe to 16 averages improves the SNR by 4 making the signal clearly visible.
This is only possible to do if your signal repeats in time.
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The noise reduces by square root of the averages used. The SNR increases by the same factor, after 100 averages the SNR went from 1 10 as expected
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In the averaging we did above we assumed the noise was random (incoherent) and normally distributed.
Is this always the case?
An interference signal might be repeating and so is not random – it has some coherence with your measurement system.
Example might be triggering (q-switch) noise in laser experiments or pick up from clock signals in electronics chain. This noise will not average as it occurs at the same time in each measurement window. (it is coherent)
Only incoherent noise averages away
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