Choice of PSD for SNR

Data Analysis
1

Dear colleagues,

I would like to ask which PSD shall I use when calculating SNR. Currently I came up with two possible methods:

  1. When calculating the SNR between original template and raw data, use the PSD from raw noises:

    スクリーンショット 2024-05-21 210013
    スクリーンショット 2024-05-21 2100131424×557 118 KB

  2. When calcluating the SNR between whitened template and whitened data, use the PSD from whitened noises:

    スクリーンショット 2024-05-21 210112
    スクリーンショット 2024-05-21 2101121388×565 80.6 KB

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?

2

Hi! Thank you for the question.

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.

Good luck!

3

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.