I am currently trying to use induced EEG and evoked EEG for Granger causality,
so I tried to separate the two from a raw EEG. (this experiment is SSVEP in 32Hz)
From what I have learned (and hopefully I understood it correctly)
Evoked EEG ≈ trial averaged ERP
Induced EEG ≈ Raw EEG - trial averaged ERP

To make sure I did everything right and to check if Evoked power and ERP are similar,
I got frequency value (power) from Raw EEG, Induced EEG, and ERP using fft in Matlab.
Then I got Evoked power by subtracting Induced Power from Raw EEG power.
Picture includes frequency domain of Raw EEG, induced EEG, ERP, and evoked power.

As it is clearly seen from the picture,
evoked power is the smallest in 32Hz and evoked power is a little different from ERP power.

Since this experiment has a stimiulus onset, I expected evoked power to be bigger, but induced power was actually much bigger than I expected.
Maybe there was a millisecond difference in stimulus onset time causing the induced power to look bigger, but I couldn’t prove whether I just used a wrong method of getting induced EEG or not,
which is why I decided to ask some questions on related topics.

Sorry for a long explanation. Following are the actual questions that I have:

Is my method on separating Induced and evoked power right?

I realized that ERP and evoked power are a little different… can I consider ERP to be evoked EEG for Granger causality?

If the method is right, can I use induced EEG (from this method) for Granger causality?

Is it possible to convert Evoked power (by this method) to Evoked EEG?
(I used ifft given by matlab but because power value loses imaginary number ifft doesn’t work properly).

If ifft does not work, is there an alternative way to convert power to a signal?

Any advice is really appreciated.
Have a great day and thank you.

Hi YES. Interesting analysis; I’ve never tried (or seen, afaik) an investigation of phase-locked and non-phase-locked SSVEP. The thing to keep in mind is that non-stationarities in the EEG – including time-varying fluctuations in frequency (even if subtle) and amplitude – are averaged out in the ERP but are captured by the “induced” spectrum. So I’m not surprised that the induced SSVEP power is still 3x larger than the ERP power.

To your questions:

That’s a difficult question to answer. The method you described is correct under the assumption that “ERP = evoked” and “residual = induced.” That’s the assumption that I (and many others) work from, but it’s a debated position. I’m not really sure the brain makes that distinction.

The ERP and evoked power are similar, although the ERP is more closely related to ITPC.

Yes.

You could subtract the full Fourier spectra (that is, the complex values that fft() returns) instead of the power values. That preserves the amplitude and phase information, which you need to get back into the time domain.

See above. But mostly people use the ERP as the evoked part of the signal.

Since the method seems correct in getting a non-phased locked value (which I will still have to consider whether I will define it as induced or not), I will try out the granger causality.

By the way I might not have clarified the question 4 enough… sorry for the confusion;;
I considered keeping the data format to complex number, but I wanted to average Induced FFT before subtracting from Raw EEG.
When I averaged induced FFT (in complex format), the complex number seemed to cancel out unless I changed it to a power value.
Thus I figured that induced FFT has to be a real value for averaging to work.
I used “mean” function to average induced FFT between trials.

So to clarity my question :
Is there a way to average complex numbers without canceling them out?
If not is there a way to preserve/extract the amplitude + phase information from a power value?

If I can’t get evoked EEG by doing ifft on evoked power, I plan to simply use trial averaged ERP as evoked EEG for Granger causality.

Averaging complex Fourier coefficients is fine. The coefficients will cancel is the phases are opposite (e.g., 0 and pi radians) and the amplitudes are equal.

I think I have a video on YT about averaging complex Fourier coefficients vs. averaging power values. Normally I would recommend averaging power values, but you need the complex values if you want to apply the ifft. Averaging the single-trial Fourier coefficients then ifft is the same thing as the ERP.

In 32Hz, Induced EEG power is bigger than the Total (Raw) EEG.
Maybe I screwed up the code or did the math wrong, but I just can’t figure out what the problem is.
May I get an explanation on this weird result?