[Eeglablist] Concerning the definition of ERSP

[Thomas Ferree]

Aleksander,
I can't speak for the history, but conceptually it makes more sense to meto
average across epochs before taking the difference.  First, the power
spectrum computed from a single trial has high variance.  Dividing by a
single trial spectrum could potentially involve dividing by some very
small numbers at certain time-frequency points, which would inflate
the importance of that trial in the average.  Second, the statistical theory
of power spectral estimation states that the log of the trial-averaged
power is chi^2 distributed.  So taking the difference of those averages
is taking the difference of two approximately normal distributions,
which makes sense.  There may be other considerations that I am
overlooking.  I will be interested to hear what others comment.

-- 
Thomas Ferree, PhD
Department of Radiology
UT Southwestern Medical Center
Email: tom.ferree at gmail.com
Voice: (214) 648-9767

On Thu, Jul 30, 2009 at 6:09 AM, Aleksander Alafuzoff <
aleksander.alafuzoff at helsinki.fi> wrote:

> Hi,
>
> While (re-)reading Makeig's 1993 article, which introduced the
> ERSP-measure, and Delorme & Makeig's 2004 EEGLAB article, I noticed a
> slight discrepancy in the way ERSP is defined. In case I've failed to
> take something into account or misunderstood the articles, please
> correct me.
>
> In Makeig's original article the "mean subject ERSP" is the average of
> baseline normalised epoch/trial ERSP's, where each epoch's time
> localised spectra are normalised by that epoch's baseline. In the more
> recent EEGLAB article ERSP is defined as the mean square amplitude of
> spectral estimate F_k (averaged over epochs k) divided by the mean
> baseline power spectrum*.
>
> Conceptually this is a big difference: the 1993 ERSP is in principle
> defined for individual epochs, while ERSP according to the 2004
> article is only defined relative to a set of epochs. In general the
> two definitions would also seem to give slightly different estimates
> of the "spectral perturbation", although, if we assume that the
> underlying baseline power spectrum is constant, the definitions are
> equivalent.
>
> At face value, the older ERSP defintion, where each spectral estimate
> is normalised relative to the local baseline, would seem more
> appropriate, since it seems inevitable that there must be some
> variation in the baseline during any experiment taking more than a few
> minutes (if for no other reason than a drop in subject alertness). Why
> then does EEGLAB use the latter definition (in both the article and
> the code as far as I can see)? The difference between the two ERSP
> estimates would seem to be quite small, so is there perhaps a
> computational advantage in the latter formulation?
>
> * In both articles the values are also log-transformed, but as far as
> I can see this is irrelevant for the current concern.
>
> --
> Aleksander Alafuzoff
> Research assistant
> Cognitive Science Unit,
> University of Helsinki
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