Personaly, I think both of them are fine. However, in GWOSC tutorial 2.2, it seems that the code calcuates SNR (in match-filter) between whitened noise and unwhiten template using whitened PSD. Is there any misunderstanding?

I like the explanation of the SNR calculation in the FINDChirp paper.

One can say either:

The SNR is computed as an inner product between whitened strain and a whitened template

OR

The SNR is computed as an inner product between “raw” strain and “raw” template, weighted by the inverse of the PSD

I would say “When calculating the SNR between original template and raw data, use the PSD from raw noises” is a correct description.

I took a quick look at the tutorial. I am sorry, but I disagree with how you’ve described what’s presented there. I see the “conditioned data” used in the SNR calculation, and in the PSD calculation. The conditioned data in this tutorial is not whitened.

Thank you very much for the reference and pointing me out. I missed the line doing filtering in the code and thought the PSD and the singal weren’t consistent.