# Coherence function

1. Aug 5, 2009

### fisico30

hello forum,

coherence function and correlation functions are the same thing.
If we consider a sinusoidal signal like cos(t), and we calculate the correlation function, we obtain a periodic function. That means that in some cases cos(t) and cos(t+tau) are very similar, for some other time delay tau values they are opposite, for other completely not correlated.
As long as there is a constant in time relationship there should be high correlation: even if the signal cos(t) and its shifted version are not very similar, they are interlocked in their phase behavior.....the correlation value for that particular shift tau might not be maximum. but the interlocking is still there....
The correlation function seems to just express the degree of similarity and not highlight the phase interlocking...

If cos(t) is expressed as exp(i*t) and the correlation is calculated, we get that the exp(i*t) and exp(i*t+tau) are correlated for all time delays tau: the magnitude of the correlation function (which is complex) is a constant for all tau....

All this to say that if we consider the real function, the correlation function is a real function whose value is indication only of the similarity between the function and its shifted version. There is not mention of the inter-relationship, the constant in time phase difference (which is the actual measure of the coherence)...
If the real function is expressed as a complex exponential, we get a correlation function with constant magnitude for all tau, to indicate the coherence (constant phase relation).
Looking for similarity instead, we need to look at the instantaneous magnitude of the complex correlation function....
IS this correct?

thanks
fisico30