Estimating the power in EEG frequency bands

[Suresh Muthukumaraswamy]

Hi Fieldtrippers,
    A late follow-up to this topic. I have recentrly been musing over how to
get a "clean" measure of the non-phase locked activity. I have tried
subtracting the ERF out prior to time-frequency computation but this
produces quite a bit of artifact...presumably since the single trial data
will have considerable ;atency "jitter"
   The comments from Christian below make sense ( I think) why simply
subtracting the two time-frequency power representaions is not valid. But I
wonder would this subtractive approach be valid if one worked with the
magnitude of the signal rather than power..omitting all the squaring operations?
  If this right theoretically, how to achieve this in Fieldtrip?. Would
setting cfg.output = 'fourier then abs'ing the output work. My suspicion is
no since the summing is being done first here. Alternatively, does one need
to hack the code to return the magnitude.

Thanks for your help on this and sorry for waking old threads :)

   - Suresh   

On Fri, 23 Feb 2007 01:44:59 +0100, Christian Hesse
<c.hesse at FCDONDERS.RU.NL> wrote:

>One further comment (please see below):
>
>> 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
>>
>Note that the other crucial thing to consider here is that you are in  
>one case averaging power over trials over trials:
>
>E[ (Induced^2)  ] =  E[ (Phase + Non-Phase)^2 ] = E[ (Phase^2 +  
>2*Phase*Non-Phase + Non-Phase^2) ] = E[ (Phase^2) ] E[ (Non- 
>Phase^2) ] + E[ 2*Phase*Non-Phase ]
>
>this is why taking the square root of sqrt(Induced^2) does not give  
>(Phase + Non-Phase) but sqrt(E[ (Phase+Non-Phase)^2 ]).
>
>in the evoked case you are taking the power of the average amplitude
>
>Evoked^2 = E[ Phase ]^2  (---> note the ^2 on the outside of the sum)
>
>so in subtracting you are actually assuming that E[Phase]^2 = E 
>[(Phase)^2] which is unlikely to be accurate the case in finite samples.
>
>Hope I have not confused others (or myself) here.
>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
>----------------------------------------------------------------------
>
>
>
>
>Date:         Thu, 22 Feb 2007 15:52:56 +0100
Reply-To:     Marcel.Bastiaansen at fcdonders.ru.nl
Sender:       FieldTrip discussion list <FIELDTRIP at NIC.SURFNET.NL>
From:         Marcel Bastiaansen <Marcel.Bastiaansen at FCDONDERS.RU.NL>
Subject:      Re: Estimating the power in EEG frequency bands
In-Reply-To:  <001d01c7568f$4b0d1890$0202fea9 at D3K61L91>
Content-type: text/html; charset=ISO-8859-1

Dear Thomas,

This is indeed the approach that I have followed succesfully a couple of
times (e.g. Bastiaansen et al., JOCN 2006), although the terminology that
you are using is somewhat confusing. I (and I guess most people) would refer
to induced activity as that part of the EEG that is non-phase-locked, so I
would restate your equation to:
induced = EEG - evoked.

However, there is a drawback to this approach, since it assumes that the ERP
is absolutely stationary over trials. This is not the case in reality (e.g.
subjects' attentional level or other states may change from trial to trial,
giving rise to variability in the single-trial ERPs). This means that by
subtracting the average ERP, one may introduce frequency components in the
residual EEG that were not present before. Klimesch, and Kalcher and
Pfurtscheller, have come up with ways of scaling the average ERP so as to
yield a best fit of the average with each single-trial ERP, but also that 
approach may be sub-optimal.
My latest way around the problem is to run a TF analysis on the untreated
EEG (containing both evoked and induced activity), and comparing this to a
TF analysis of the subject-averaged ERPs (the evoked activity alone).
Qualitative differences between the two analyses can now only be attributed
to induced activity.

Marcel

Thomas Thesen wrote:
>
> Hi FieldTrippers,
>
>  
>
> 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?
>
>  
>
> So if
>
> Induced = Phase + Non-Phase
>
> And
>
> Evoked = Phase
>
> Then
>
> Non-Phase = Induced – Evoked
>
>  
>
> Or does the fact that this is a linear operations on data that have been
constructed through a non-linear process render this somehow invalid? It has
certainly been done before. Your comments would be much appreciated.
>
>  
>
> Cheers,
>
> Thomas