From: dbd on 17 Mar 2010 02:47 On Mar 16, 10:19 pm, Dirk Bell 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 wrote:> On Mar 16, 10:19 pm, Dirk Bell 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 wrote:> On Mar 16, 10:19 pm, Dirk Bell 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 wrote:> On Mar 17, 2:47 am, dbd wrote: > > > > > On Mar 16, 10:19 pm, Dirk Bell 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 wrote:> On Mar 17, 7:05 am, Dirk Bell wrote: > > > > > > > On Mar 17, 2:47 am, dbd wrote: > > > > On Mar 16, 10:19 pm, Dirk Bell 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