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This question is about SNR in the context of EEG. (a related question about SNR)

I am interested in calculating The SNR of an ERP. My motivation is: To calculate the "signal-to-noise ratio" and from this to extract the information (how?) on how many trials are needed to construct a stable ERP.

my Main question is: how do I calculate and SNR for such scenario ?

some more explation about EEG and ERP are enclosed: EEG:

The on-going electrical activity of the brain measured from scalp electrodes is called the electroencephalogram or EEG. within the EEG is a signal which is more revealing about information processing in the brain. This signal can be obtained by time-locking the recording of the EEG to the onset of events such as a person reading a word on a computer screen, listening to a musical note played on an instrument, or viewing a picture in a magazine. The resulting activity is called an "event-related potential" (ERP)

SNR:

The number of trials necessary to obtain an ERP depends on a number of factors, the most important being the "signal-to-noise ratio", that is, the relative size of the signal (the ERP) relative to the size of the noise (the background EEG). In cognitive experiments 30 to 50 stimulus presentations are typically required to obtain a good clean average ERP.

from: http://neurocog.psy.tufts.edu/images/erp.htm

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    $\begingroup$ Can you get a "noise" estimate by doing a lengthy average of the EEG power when no ERP's are happening? $\endgroup$
    – Jim Clay
    Commented Mar 7, 2012 at 13:57
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    $\begingroup$ You should use the definition of SNR and methods of measuring it as given in your sources. As this question and the ensuing discussion notes, there might be different definitions of SNR, and so you need to pick one convention and follow it. $\endgroup$
    – Dilip Sarwate
    Commented Mar 7, 2012 at 14:41
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    $\begingroup$ This sounds a bit "Chicken and egg" to me . . . or should I say "chicken and EEG". Joking aside, I guess you need to pilot to see how many trials it will take before your ERP is usable. That will give you an idea of how noisy your data is. Unless you know the noise or the ERP you are trying to extract a priori, you will have to perform the averaging to find out. I'm guessing this value will be affected by both the experimental setup and the design of your particular experiment. I'm guessing piloting is the key . . .but that is a guess and hence why this is a comment and not an answer. $\endgroup$
    – learnvst
    Commented Mar 8, 2012 at 1:08
  • $\begingroup$ All, thanks for your comments! i will follow your suggestions. $\endgroup$
    – Dov
    Commented Mar 8, 2012 at 10:43

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First you have to clearly define what you mean by "noise". Is simply the electronic noise in your measurement system or is it also brain activity that's not related to your stimulus.

One easy way to determine SNR is to compare the signal level during a stimulus with the signal level without stimulus. If noise and signal are uncorrelated you can determine the signal level through energy subtraction and thus determine the SNR.

Depending on your noise definition, this may not be practical cause you can't easily shut off the brain of the subject :-).

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  • $\begingroup$ +1 That is why I suggested piloting in my comment above. You hit the nail on the head with the comment about whether the signal and noise are correlated. $\endgroup$
    – learnvst
    Commented Mar 8, 2012 at 19:05
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    $\begingroup$ SNR = P_alive/P_dead $\endgroup$
    – endolith
    Commented Mar 30, 2012 at 14:34
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here [PDF] is a doctoral thesis that explains how to do it (go to section 5.3.7. (AEP quality))

from the paper: "Traditionally the SNR is defined as the power of the signal at a peak latency of interest divided by the mean power of the activity in the baseline period"

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  • $\begingroup$ Any change of getting the paper title? Link is dead. $\endgroup$
    – AndrejaKo
    Commented Jul 12, 2016 at 16:51
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This is an unacceptable definition of SNR. I don't know how the author of this thesis uses the word "traditionally"! SNR is only defined as the power of the signal to the power of the noise in the same band of frequencies, and measured in the same time interval. Please refer to https://en.wikipedia.org/wiki/Signal-to-noise_ratio. I have not seen any other definitions. Can anyone give any standard reference (reviewed) for the above "traditional" reference? If there is no reference that could be found, then it is simply an invalid definition.

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