# What is QEEG technically, and how is it computed?

I've been working with EEG signals for a while. I wonder how to compute QEEG (or Brain Map) representation. I think it is extracted from raw EEG and I want to know what is technical method for QEEg extraction? Is it simply a Fourier transform or something complicated is utilized? In a nut shell: - What is qEEG exactly and how to compute it technically to come up with something like in figure above?

I feel it should be related to short time-Fourier transform.

• I think there are two separate questions here: (a) What is qEEG? (b)How to generate plots like the one shown? (a)There's no standard definition for qEEG - it may refer to any quantitative metric extracted from EEG signals, usually with Fourier or wavelet analysis. (eg. energy in a certain frequency band) (b) Take a look at this: martinos.org/mne/stable/generated/… Feb 7 '17 at 19:58
• @AtulIngle , thanks for the comments, you probably are right here. The link is indeed useful, however I did not mean to ask its implementation, I want a signal processing point of view of qEEg, so I think these two are both sides of a coin. I wish you provided detailed of your comment as an answer, it is on the track! Feb 8 '17 at 12:06

qEEG or quantitative EEG is an umbrella term that encompasses many different signal processing methods that compute a number/statistic/quantitative biomarker from EEG signal traces. Algorithms usually boil down to some form of spectral analysis either using Fourier transforms, or wavelets.

The images in shown in the question are most likely generated through spectral analysis of individual EEG channels. In your figure, it seems like the author chose Delta to mean 1-3.5Hz. Some authors use Delta as all frequencies <4Hz. (https://en.wikipedia.org/wiki/Electroencephalography)

To compute the contribution of each band, one resorts to standard power spectrum analysis techniques. For example, for a given EEG channel $i$, the Delta qEEG biomarker value can be computed as:

$$\mbox{Delta}_i = \frac{\int_{1}^{3.5} P_{i}(f) df}{\int_{0}^{\infty}P_i(f)}$$

where $P_i(f)$ is the power spectral density of the $i^{th}$ EEG channel signal. In practice, you can use, say, Welch method to estimate $P_i(f)$ from sampled EEG channel traces, the integrals will get replaced by sum over frequency bins, and you'd only go up to Nyquist.

Repeat this process for each frequency band, for each EEG channel to get sequences $\{\mbox{Delta}_i\}_{i=1}^N$,$\{\mbox{Theta}_i\}_{i=1}^N$, $\{\mbox{Alpha}_i\}_{i=1}^N, \cdots$, where $N$ is the number of EEG channels.

The final step is to map these numbers on the image of the scalp. This is a visualization step which involves interpolation. You can use a tool like this: https://martinos.org/mne/stable/generated/mne.viz.plot_topomap.html#mne.viz.plot_topomap or https://www.nbtwiki.net/doku.php?id=tutorial:plot_a_time-frequency_representation_and_power_spectrum_of_a_single_channel#.WJtLMxC2pJI.

• Thanks, you answer is illuminating. There only one thing, if we consider whole spectrum artifacts might intervene and contribute to band power, could the EEG signal be sentimentalized into windows and spectrum of each considered? (to produce something like video and also avoid artifacts) Feb 8 '17 at 17:05
• This might be a good question for an area expert in EEG processing. As a signal processor, I see no reason why that can't be done. What you just described will add a "time" axis to the image in your question and then you can play a movie of these images. Then again, I'm not sure what you mean by "spectrum artifacts". Perhaps you can try a few different methods for power spectrum estimation instead of the simple Welch method. Feb 8 '17 at 17:16