I am trying to understand coherence function calculation. I am working with a non-linear system without any noise. Coherence function is defined as:
I understand that coherence is 1 for N=1, but I don't understand why coherence is different with segmentation? As far as understand with segmentation without any noise in system, each segment should give same values and them coherence will go to 1 again. I think I am missing something. I am quite new to this subject. Could anyone help me with this? Is there any good reference related to this where it has proved that why coherence is different with segmentation? I have gone through the following questions: Optimal segment length for coherence estimation and Magnitude-squared Coherence calculation inconsistence but I still it is not clear to me.