Dear EEG community,

after working through most of ANTS (your book is great Mike! It helped me a lot!!!), I still have a few points that are unclear to me or are described or explained differently in other literature.

My problem(s)/question(s) refers to the Power Spectrum or Power Spectral Density and its units and the calculation of the power of frequency bands.

First to the Power Spectrum / Power Spectral Density. Is there a difference between the Power Spectrum and the Power Spectral Density? Or are they simply two terms used synonymously? I have the feeling that the terms are often mixed up in the literature.

To describe my further problems/questions about the units and the calculation of the power of frequency bands, I would like to present an example.

I have a resting state EEG recording of 120s with a srate of 1024Hz and a total of 19 electrodes (data points per electrode = 122.880 in µV).

**I am interested in the question how high the power in the theta-band (3.5 - 7.5Hz) is.**

My steps (I think they are the same steps that EEGlab does) that I did with MATLAB:

- Preprocessing (filter, …, ICA, …, and so on) to get clean data
- Separate the data (19, 122.880) into consecutive epochs of 2s with 75% overlap. → my data has now 3 dimensions (19, 2048, nb_of_epochs)
- after that I applied matlabs detrend() function to the epochs to remove polynomial trend
- after that I applied the hamming window (length: 2048) to the epochs.
- then I calculated the fft: data_fft = fft(data, [], 2) which is of course complex valued and still has the dimensions (19,2048,nb_of_epochs)

**Is it correct that the units of the Fourier coefficients of data_fft (and data_fft represents the amplitude spectrum) are µV/√Hz Or is it just µV?**

- then I calculated the power: data_power = data_fft.*conj(data_fft) and after that I averaged data_power across the epochs. Then I have data_power(19, 2048) which is real valued and which has 2 dimensions.

**Is this now the so called Power Spectral Density? What are the units now? Is it µV^2/Hz or just µV^2?**

- My initial question was how high the power is in the theta-band (3.5-7.5Hz). For this I averaged the power values of data_power, which are in the range of 3.5-7.5Hz (EEGlab does the same).

**Is this now the so called Power Spectrum? The units should not have changed, because I only took the average. I have read that another possibility is to calculate the integral under the area of 3.5-7.5Hz in the Power Spectrum/Power Spectral Density. What is the difference between the two methods? How do I interpret the results?**

At this point I would like to mention that I have not (yet) applied the two scaling options (Divide coefficients by N, double positive coefficients). As I have understood, EEGlab does not do that either and just takes the decibel conversion (10*log10(data_power)). I left out the dB conversion in my example.

Sorry for the long text and the many questions I would be happy if some of them could be answered.

Thanks in advance!

Niko