mscohere function : coherence always 1 ?

Hi everyone, i want to calculate the coherence between two different signals. And also to compare the coherence results for noise-free signals and noisy signals. In order to understand the working principle of "mscohere" function, i started by using a rectangular window (same length as the signals) with no overlapping for the signals first. Supposingly, based on my understanding i should get a different coherence results for both the noisy signals and noise-free signals but i always got my coherence = 1 for both noisy signals and noise-free signals. Even if i changed the window type to hann (for example), i still got coherence equals to one. The coherence results will only be changed if the signals are segmented > 10 % (for example), when i change the window length. Does anyone know what is the exact working principle of the window function in the mscohere? what window length should i choose and why? some references suggest using hann window with 50% overlapping but why? ____________________________________________________________________________________________ 1st set (noise-free) : s1 and s2 are my signals and have similar waveform but are different from each other with a time delay.

2nd set (noisy) : + noisy (random) signal to s1 and s2

[cxy,freq]=mscohere(s1,s2,rectwin(nfft),0,nfft,fs);

Answer 1

[Hugo Nunes]

The coherence is statistally meagninfull when you use an average of several windows. See link bellow:

https://dsp.stackexchange.com/questions/10012/magnitude-squared-coherence-calculation-inconsistence