Simulated observation of gravitational wave data

I want to simulate a section of gravitational wave data containing noise. Based on literature and tutorials, my understanding is to simulate noise and gravitational wave signals separately, and add them in the time domain accordingly. But does the real gravitational wave signal have a certain coupling with noise, so it cannot be simply added directly?

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That’s a great question!

No - real GW signals do not couple to the noise, so it is OK to add simulated signals directly to the data.

However, it is important to account for the “antenna pattern” of the detector, before adding a simulated signal to the noise.

You can see some example code to do that using pyCBC.

And, you can look for explanations of the Antenna Pattern in online resources, such as this: