[Eeglablist] Concerning the definition of ERSP

[Aleksander Alafuzoff]

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