View Full Version : Coherency Measures

Steve Morrison
01-09-1997, 04:17 AM
To all subscribers,

We recently have been looking closely into the use of frequency analysis of
continuous time series biological data and have (apparently) come across
some what of a misconception/misinterpretation within the movement domain
concerning the use of the term "coherency".

Our understanding is that coherency represents a measure of the relation
between the cross-spectral power (squared) and the auto-spectra of each
signal. In most movement control articles examining coherency, it has been
likened to an analogous form of correlation in the frequency domain, and it
is generally inferred (we think incorrectly) that this measure does not tend
to include any details about the phase relation inherent in the data. This
latter part of this statement, concerning the phase involvement, appears to
be a general assumption bourne by a direct comparison of this technique to
correlation techniques in the time domain.

Under this assumption (with no phase relation), one would expect two signals
which retain the same modal frequency to be reasonable coherent. However,
this is not shown to be the case in many situations (For a particularly good
example of this, see the figure in; Marsden et al, (1969) Electrenceph Clin
Neurophys, pg 181). In these cases, two signals which oscillate at the same
frequency, do NOT have high coherency, indicating that some part of the
calculation of these varibles which may up the coherency value probably
includes details about the phase relation between the signals. For example,
two processes may oscillate at the same frequency (and hence have a "high"
cross-spectral arrangement between the signals) but the degree of coupling
(in phase/out of phase or no consistent phase relation) would effect the
overall coherency value.

Unfortunately, most software packages do not provided enough information as
to how the coherency/phase/power spectral denisty values are calculated so
one often has to assume that they are following the general formula
guidelines (set out in such texts as Jenkins and Watts, (1968) & Glaser and
Ruchkin, (1976)).

The question we would like to resolve is whether the phase relation is an
important component to consider when interpreting analysis of the coherency

As usual, I will summerise all replies.


Steven Morrison
Dept Of Kinesiology
Penn State University
State College, PA 16802

email: sxm36@psu.edu
Phone: (814) 865-9544