Processes/Transforms involved to get brainwave data from raw EEG? (Autocorrelation confusion)

Question

Not clear on what the autocorrelation function of raw EEG means physically

why can't you take the FT of a the EEG itself and get frequency data?

With BCI & basic electrode setups you can understand your brain activity: neuron-firing --> EEG voltage reading --> brainwave readings

How I understand that this is done:

Fourier Transform: Operation bringing you from TIME domain to FREQUENCY domain

• Time Domain: EEG raw ... x= time , y= volts
• Frequency Domain: brainwave data... x= frequency, y=intensity

Fourier Theorem ... basically that every line/wave can be broken down into pure components (single frequency sinusoids)

First you need the autocorrelation of the raw EEG

- Correlate EEG signal with itself - compare EEG signal at one time pt -- to another time pt... shifted tau

- Get the nature of the EEG signal through time ... how voltages are shifting

FT of Autocorrelation --> PSD We treat the signal as stationary, even though in reality it is moving in time and apply a windowing method like the Welch's Method .. and slide this window along the entire EEG signal.

Outcome is a PSD plot <-- which gives intensity of each frequency band

Thanks!

Answer 1

And the power spectral density is the Fourier transform of the autocorrelation.

I don't know about EEG data, but you can compute autocorrelation either in time domain or frequency domain. For instance if you need only a few samples of the autocorrelation it may be computed more efficiently using inner products than it would by $FFT^{-1}(|FFT(x)|^2)$. You know that the autocorrelation and the power spectral density are a time-frequency pair, so if the nature of information harmonic responses, oscillation modes, (power spectral density). But if the nature of the signal is chaotic with some dispersion (memory effect) you use the time domain (autocorrelation). autocorrelation are very good to analyze channel response in communication, and the signals in the brain are communication signals, so to me it makes sense to use that instead of frequency domain that could be used for identifying vibration in an engine for instance.

Answer 2

Autocorrelation reveals periodicity patterns in the data. Taking an FFT will reveal the frequencies of the patterns.

(don't understand why this is relevant enough ... will add more later)