FPGA Central

Hello,

I hope this doesn't cause any frustration or breaks any group rules,
but I'm posting an excerpt from another thread to broadcast my question
to a potentially larger audience. Regarding the coherence function, or
magnitude squared coherence as it were:

The coherence result is bounded between 0 and 1 mathematically. This
is due to what's called the cross-spectrum inequality (see Bendat and
Piersol, Engineering Applications of Correlation and Spectral Analysis,

2nd edition, Wiley and Sons, 1993 - page 53 eq 3.42), which states
that the magnitude squared of the cross spectrum is always less than or

equal to the product of the autospectra. This is the foundation for
the coherence function on the next page of the text. There, as well
as almost everywhere else I've seen it, the function is called the
"magnitude squared" coherence, denoted by gamma squared. This
function is also referred to as the "coherence function" so it is
definitely confusing. The equation is the same as the one used in
the Matlab function mscohere and quoted above, |Sxy(f)|^2/Sxx(f)Syy(f)
where Sxy is the cross spectrum and Sxx, Syy are the respective
autospectra.

Interestingly, Matlab recently replaced its previous cohere.m function
with the mscohere.m function, called magnitude squared coherence, I'm
guessing to help clear up this confusion for their users (I don't
have a copy of mscohere.m, and short of installing the latest matlab
version, can anyone suggest where I may be able to find the m-file
source code?). I am still unsure of the implications of this
distinction, but I do know that in most engineering applications, the
magnitude squared coherence is the metric that is used to estimate
coherence, i.e. the stability of phase between two signals. Can anyone

comment on this? What is the difference between coherence and
magnitude squared coherence? Is it just different nomenclature for the
same metric or is there a quadratic relationship between the two?
I'm assuming it's as simple as the names suggest but I'd love to know
more about the differences between the two from an application
point-of-view.

Thank you,
Cliff

The coherence in my book is like cross-correlation - only it is a
function of frequency. So two signals maye have a strong coherence at
low freqs but not at high frequencies.

I tend to think the other way round - it woudl seem more difficult to
calculate coherence than MSC since coherence has a square root in it.
You shoudl just be able to square the magnitude of coherence to get MSC
(hence the name!)

Tam