# Estimating the power in EEG frequency bands

Christian Hesse c.hesse at FCDONDERS.RU.NL
Fri Feb 23 00:40:12 CET 2007

```Hi Thomas,
> Following up on this conversation. It seems that the ‘induced
> activity’ contains both phase-locked and non-phase-locked activity,
> whereby the ‘evoked’ activity contains only phase-locked activity.
> Is it then kosher to separate these components by linear
> subtraction? For example, if we first compute the ‘induced’
> activity by averaging power over individual trials, and from that
> subtract the ‘evoked activity’ (calculated based on average
> response) to get the induced activity without any phase-locked
> activity?

It is not correct to subtract because computing the induced and
evoked power spectra involves squaring signal amplitudes (a non-
linear operation), and hence, taking your terminology to refer to the
instantaneous amplitudes of the signal components (this applies to
any time-frequency tile)
> Induced = Phase + Non-Phase
>
> And
>
> Evoked = Phase
>
> Then
>
> Non-Phase = Induced – Evoked
>
>
what you actually get from spectral or time-frequency analysis is the

Induced^2 = (Phase + Non-Phase)^2 = Phase^2 + 2*Phase*Non-Phase + Non-
Phase^2

Evoked^2 = Phase^2

Then

Induced^2 - Evoked^2 = 2*Phase*Non-Phase + Non-Phase^2  AND NOT Non-
Phase^2

This bit of high-school algebra shows quite clearly that even if you
had a perfect estimate of Evoked and Induced power (which you of
course in practice do not have due to a finite number of trials,
amplitude non-stationarities, artifacts and noise) it is not possible
to obtain an estimate of Non-Phase^2 using time-frequency analysis,
averaging and subtraction.

Cheers,
Christian

----------------------------------------------------------------------
Christian Hesse, PhD, MIEEE

F.C. Donders Centre for Cognitive Neuroimaging
P.O. Box 9101
NL-6500 HB Nijmegen
The Netherlands

Tel.: +31 (0)24 36 68293
Fax: +31 (0)24 36 10989

Email: c.hesse at fcdonders.ru.nl
Web: www.fcdonders.ru.nl
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