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

values.

As usual, I will summerise all replies.

Thanks

Steven Morrison

Dept Of Kinesiology

Penn State University

State College, PA 16802

email: sxm36@psu.edu

Phone: (814) 865-9544

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

values.

As usual, I will summerise all replies.

Thanks

Steven Morrison

Dept Of Kinesiology

Penn State University

State College, PA 16802

email: sxm36@psu.edu

Phone: (814) 865-9544