[Eeglablist] Coherence for Single-Trial Data

[benjamin.deen at yale.edu]

Hi,

I have a question regarding EEGLAB's event-related phase coherence (ERPCOH)
measure, calculated on data with only a single trial.  According to the
definition of ERPCOH given in "EEGLAB: an open source toolbox for analysis of
single-trial EEG dynamics including independent component analysis" (Delorme
and Makeig, Journal of Neuroscience Methods 134 [2004], 9-21), it would seem
that this quantity can only have magnitude less than one when multiple trials
are used.  With multiple trials, ERPCOH will sum to about one if there is a
phase relation between the signal from two channels (at a given frequency and
point in time) which is consistent over trials; otherwise, the cross-spectral
densities for each trial will point in different directions in the complex
plane, cancelling when summed and resulting in a low ERPCOH.  But the
definition seems to clearly imply that coherence calculated on data with only a
single trial will have unit magnitude at all times and frequencies, regardless
of the input signals.  However, when I run pop_crossf via the EEGLAB gui, and
input single-trial data, I get coherence plots that are certainly not always
one (in fact, they are often nearly always zero, and seem to have meaningful
variation).  How can this be, if the definition given in Delorme and Makeig
(2004) is what pop_crossf is using to calculate coherence?

Thanks,

Ben