Look at the Zurich Industrie paper

which explains how the correlation integral is done in the time domain.

Zurich Industry link

attached is the equation.

We see that to do the correlation in time we slide

one signal with respect to the other.

If you reverse the phase of the signal, you will not

change anything, you will always have to slide the signals.

Phase slide to calcul correlation time function

In fact, what is done is the Fourier transform

of the correlation in time which gives "by chance"

the denoised FFT.

which explains how the correlation integral is done in the time domain.

Zurich Industry link

attached is the equation.

We see that to do the correlation in time we slide

one signal with respect to the other.

If you reverse the phase of the signal, you will not

change anything, you will always have to slide the signals.

Phase slide to calcul correlation time function

In fact, what is done is the Fourier transform

of the correlation in time which gives "by chance"

the denoised FFT.

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