[Eeglablist] Coherence for Single-Trial Data

[arno delorme]

Dear Ben,

> 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?


What you are looking at is probably the bottom panel of the crossf  
function output. The upper panel is uniform and equal to 1. The bottom  
panel is the phase and varies even if there is only one trial.

Best,

Arno