Using moving average as the mean amplitude to find residual amplitude

[md-arif-shaikh]

This could be an optional method that we can add later to the library.

Idea

• This is nothing new. We have discussed this more than once before deciding to use the quasicircular amplitude as reference amplitude to subtract from the eccentric amplitude to get the residual amplitude which we use to find the location of the extrema.
• The idea is to use a moving average of the amplitude itself. The problem is that we need a picture of the window (let's say over an orbit) in terms of the sample points around a given data point where we want to compute the moving average. One can get an idea of the window by seeking the number of indices over which $\phi_{22}$ changes by a $4\pi$. However, we also need to be careful about the pericenter advancement which could change the averaging non-trivially.

Basic Implementation

• Over the last couple of days I tried to add a module to our library based on this idea. I am able to get a decent working method. Below I attach two plots from eob tests over one parameter set.
• Currently, it's on a branch on my local machine. will push it at some point so that it could be polished and improved later.

test_eob_vs_measured_ecc_set3_ResidualAmplitude_MovingAmplitudeAverage.pdf
test_measured_ecc_vs_time_set3_ResidualAmplitude_MovingAmplitudeAverage.pdf

This issue to come back to this in the future.