# [FieldTrip] connectivity problem

Eelke Spaak eelke.spaak at donders.ru.nl
Thu May 23 10:09:17 CEST 2013

```Dear Gabriel,

If I am not mistaken, the classical formula in Lachaux et al. (1999)
Human Brain Mapping is PLV = 1/N * | sum(exp(i * theta(t,n))) | . This
is almost the same as the formula you mention, except, importantly,
that theta is the phase difference between two signals, so the angle
of the CSD, and *not* the imaginary part.

Note furthermore that 1 * exp(i*angle(z)) is equal to z/abs(z) for any
complex z, and you see that the implementation computes the classical
formula.

Hope this helps,
Best,
Eelke

On 22 May 2013 19:36, Gabriel Gonzalez Escamilla <ggonesc at upo.es> wrote:
> Dear Fieldtrip experts,
>
> I finally understood how fieltrip computes the plv, so, my last e-mail has
> no sense now. Given say this, I have one question:
>
> I've followed the fieltrip implementation to compute the PLV, and found that
> it takes the CSD, and normalizes it for the amplitude of the replicates,
> this is to divide the csd by the absolute of the same csd, then makes an
> average of the normalized csd's, to finally take the absolute of the
> average-normalized-csd as the PLV.  I think it can be summarized to
> something like, PLV = |E( csd/abs(csd) )|
>
> I do not see the similarity with the clasical formula that appears in the
> papers PLV=| E{exp(i*I{X})} |, where I{X} is the imaginary of the
> cross-spectrum, and E|.| is the expected value; I cannot find the
> relationship between the implementation on fieltrip of the PLV and the
> formula on the papers.
>
> Can anyone explain to me the relationship between the two approaches? or
> tell me the paper where it is explained?
>
> Many thanks in advanced,
> Gabriel
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```