# How do I measure ratio of EEG frequency band for a few electrodes in decibels?

I wanted to calculate the ratio of Theta/Beta ($\Theta$/$\beta$) in decibels for a couple of electrodes in AF3 AF4 and Cz

I was able to get these in microvolts, but would like to convert them to decibels but am unsure what is the appropriate way to do so.

For instance, should I convert it like:

$$ratio_1 = 10.log\left( \frac{\Theta_{AF3} + \Theta_{AF4} + \Theta_{Cz}}{\beta_{AF3} + \beta_{AF4} + \beta_{Cz}}\right)$$

or

$$ratio_2 = 10.log\left(\frac{\Theta_{AF3}}{\beta_{AF3}}\right) + 10.log\left(\frac{\Theta_{AF4}}{\beta_{AF4}}\right) + 10.log\left(\frac{\Theta_{Cz}}{\beta_{Cz}}\right)$$

• Are you calculating the ratio of all electrode simultaneously? If yes, i think the second one is correct. – maia Dec 2 '17 at 6:07

Also note that dBs are usually defined in log10 scale ($\frac{ln(x)}{ln(10)}$), but it doesn't really matter.