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From: dbd on 17 Mar 2010 02:47
On Mar 16, 10:19 pm, Dirk Bell <bellda2...(a)cox.net> wrote:
....
>
> Dale,
>
> Interesting reference.  Using FFTs aren't they computing the frequency
> dependend coherence function rather than the normalized cross-
> correlation?
>
> Dirk

Both are defined in the first reference.
In the B&K formulation, the correlation coefficient is calculated from
covariance and standard deviation coefficients. The coherence function
is calculated from auto and cross spectrum functions.

Dale B. Dalrymple
From: Dirk Bell on 17 Mar 2010 09:44
On Mar 17, 2:47 am, dbd <d...(a)ieee.org> wrote:
> On Mar 16, 10:19 pm, Dirk Bell <bellda2...(a)cox.net> wrote:
> ...
>
>
>
> > Dale,
>
> > Interesting reference.  Using FFTs aren't they computing the frequency
> > dependend coherence function rather than the normalized cross-
> > correlation?
>
> > Dirk
>
> Both are defined in the first reference.
> In the B&K formulation, the correlation coefficient is calculated from
> covariance and standard deviation coefficients. The coherence function
> is calculated from auto and cross spectrum functions.
>
> Dale B. Dalrymple

I noticed both were combined I just didn't see the normalized cross
correlation computed with FFTs to the degree that it can be (ie.
including the normalization factor that is shift dependent).

Dirk
From: Dirk Bell on 17 Mar 2010 10:05
On Mar 17, 2:47 am, dbd <d...(a)ieee.org> wrote:
> On Mar 16, 10:19 pm, Dirk Bell <bellda2...(a)cox.net> wrote:
> ...
>
>
>
> > Dale,
>
> > Interesting reference.  Using FFTs aren't they computing the frequency
> > dependend coherence function rather than the normalized cross-
> > correlation?
>
> > Dirk
>
> Both are defined in the first reference.
> In the B&K formulation, the correlation coefficient is calculated from
> covariance and standard deviation coefficients. The coherence function
> is calculated from auto and cross spectrum functions.
>
> Dale B. Dalrymple

I noticed both were defined I just didn't see the normalized cross
correlation computed with FFTs to the degree that it can be (ie.
including the normalization factor that is shift dependent).

Dirk


From: dbd on 17 Mar 2010 14:24
On Mar 17, 7:05 am, Dirk Bell <bellda2...(a)cox.net> wrote:
> On Mar 17, 2:47 am, dbd <d...(a)ieee.org> wrote:
>
>
>
> > On Mar 16, 10:19 pm, Dirk Bell <bellda2...(a)cox.net> wrote:
> > ...
>
> > > Dale,
>
> > > Interesting reference.  Using FFTs aren't they computing the frequency
> > > dependend coherence function rather than the normalized cross-
> > > correlation?
>
> > > Dirk
>
> > Both are defined in the first reference.
> > In the B&K formulation, the correlation coefficient is calculated from
> > covariance and standard deviation coefficients. The coherence function
> > is calculated from auto and cross spectrum functions.
>
> > Dale B. Dalrymple
> ...
> I noticed both were defined I just didn't see the normalized cross
> correlation computed with FFTs to the degree that it can be (ie.
> including the normalization factor that is shift dependent).
>
> Dirk

B&K's instrument is a 2 channel real time analyzer. It is not set up
to do any possible combination of x and y, but the definitions can be
applied to any choices of x and y. Set x to your reference and slide
data through y.

Dale B. Dalrymple
From: Dirk Bell on 17 Mar 2010 18:09
On Mar 17, 2:24 pm, dbd <d...(a)ieee.org> wrote:
> On Mar 17, 7:05 am, Dirk Bell <bellda2...(a)cox.net> wrote:
>
>
>
>
>
> > On Mar 17, 2:47 am, dbd <d...(a)ieee.org> wrote:
>
> > > On Mar 16, 10:19 pm, Dirk Bell <bellda2...(a)cox.net> wrote:
> > > ...
>
> > > > Dale,
>
> > > > Interesting reference.  Using FFTs aren't they computing the frequency
> > > > dependend coherence function rather than the normalized cross-
> > > > correlation?
>
> > > > Dirk
>
> > > Both are defined in the first reference.
> > > In the B&K formulation, the correlation coefficient is calculated from
> > > covariance and standard deviation coefficients. The coherence function
> > > is calculated from auto and cross spectrum functions.
>
> > > Dale B. Dalrymple
> > ...
> > I noticed both were defined I just didn't see the normalized cross
> > correlation computed with FFTs to the degree that it can be (ie.
> > including the normalization factor that is shift dependent).
>
> > Dirk
>
> B&K's instrument is a 2 channel real time analyzer. It is not set up
> to do any possible combination of x and y, but the definitions can be
> applied to any choices of x and y. Set x to your reference and slide
> data through y.
>
> Dale B. Dalrymple- Hide quoted text -
>
> - Show quoted text -

Right. As both of us have noted, the definitions can be used. The
question of interest, I believe, is how to implement the calculation
with maximal use of FFTs, which means how to calculate the shift
dependent normalization factor with FFTs assuming it is efficient to
do so.

Dirk
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