Missing unit of Global Field Power

Hello @Raymundo.Cassani,
My apologies for opening up an old conversation. I just have a question about the mathematics behind the claim that GFP and power are equal when average reference is used.
The "std" function used to compute GFP is defined by Matlab from this documentation with the formula shown below. And the power cluster function is defined by "power = E(x.^2)/N" (formula 3).
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The mean of all the sensor values is most of the time close to zero or IS equal to zero in the case of EEG with an average reference. Therefore in the Matlab "std" formula, the variable "µ" will be 0 (formula 1 and 2). However, I still do not see how GFP and power functions could be equal when average reference is used as the power function does not have a square root and is divided by "N" not "N-1".
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Would you mind providing a mathematical explanation for this?