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Is there a general formula I could use to calculate the ideal window for the window argument in the function scipy.signal.coherence, maybe taking into account sampling rate and number of time points?

For example, if I acquired data at a sampling rate of $1.5\texttt{Hz}$ and I have $100$ time points, what window size would you recommend?

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  • It depends what frequency resolution you are happy with, i.e. how many discrete frequencies you think are relevant to you. These frequencies will span $0$ to $f_s/2$, and you will get a coherence value for each.
  • The frequency resolution is computed as $f_s/N$, $N$ being the size of the analysis window.

With that in mind, a here is an example:

$N = 10$ will give you $N/2 = 5$ values for your coherence function (the negative frequency part is discarded), at the following discrete frequencies spaced $f_s/N = 0.15\texttt{Hz}$ apart: $$0\texttt{Hz}, 0.15\texttt{Hz}, 0.30\texttt{Hz}, 0.45\texttt{Hz}, 0.60\texttt{Hz}$$

Note, you can also play around with the noverlap argument. Typical values would be $N/2$ or $N/4$

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  • $\begingroup$ Thanks a lot for the explanation, it was very helpful! What would you consider a reasonable frequency resolution to be? I'm mostly interested in very low frequencies (below 0.25 Hz). I believe matlab uses a default L=N/4.5, but I'm not sure what the rationale is for that choice. $\endgroup$
    – HappyPy
    Jan 25 at 22:34
  • $\begingroup$ I don't know your application, so you need to define what a reasonable frequency resolution is based on your requirements. You can also compute the coherence on the full $100$ points. By the way, I'm assuming you know what coherence is, you do know it's computed between two signals right? Your question mentions "data", hence my question. $\endgroup$
    – Jdip
    Jan 25 at 23:15

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