Estimating the power in EEG frequency bands

[Christian Hesse]

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  
power of your MEASURED signal

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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