Coherence of random data

Pascal Fries Pascal.Fries at FCDONDERS.KUN.NL
Fri Feb 18 12:40:56 CET 2005

Dear Laurens,

I guess terminology here is somewhat inconsistent between different authors.
I have attached a paper by Challis, in which (p. 237) he defines coherence
as we use it in freqdescriptives, while he calls the squared version
"magnitude squared coherence". Other papers call the squared version simply
"squared coherence". I guess, the best approach is to clearly state what one
is using.

The relation between coherence and coherency is clear:

Coherence  = abs(coherency)

i.e. coherency is the complex quantity, containing the information on both
the strength and the phase of coherence, while coherence speaks only to the

Best, Pascal

Pascal Fries
Principal Investigator
Neuronal Coherence Group
F. C. Donders Centre for Cognitive Neuroimaging
Radboud University Nijmegen

Adelbertusplein 1
6525 EK Nijmegen
The Netherlands

Phone: (+31) (0)24 36 10657
Fax:   (+31) (0)24 36 10989
e-mail: pascal.fries at

> -----Original Message-----
> From: FieldTrip discussion list
> [mailto:FIELDTRIP at NIC.SURFNET.NL] On Behalf Of Laurens Hogeweg
> Sent: Friday, February 18, 2005 10:54 AM
> Subject: Re: [FIELDTRIP] Coherence of random data
> Hello,
> Thanks for your extensive answer to my questions. Things are
> getting a bit clearer now around here. I have but one small
> question about terminology left for the moment:
> - R^2 = (Fxy.Fxy)/(Fxx.Fyy) (coherence)
> - R = Fxy/Sqrt(Fxx.Fyy) (coherency)
> According to Halliday et al. (1995)
> If I am not mistaken you are using R (coherency) in FieldTrip
> instead of R^2 (coherence). I think this caused a lot of
> confusion here,
> Thanks,
> Laurens
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