Interpolate amplitude and phase of SNR time series, not real and imaginary parts

Description of change

Change BAYESTAR's strategy for evaluating SNR time series from Catmull-Rom interpolation of the real and imaginary parts to Catmull-Rom interpolation of the amplitude and phase. The old interpolation method could produce oscillatory artifacts in the SNR amplitude if the data are nearly critically sampled, as is the case for early-warning BNS events. The new interpolation method is immune to this kind of artifact, and also has much faster convergence as a function of sample rate.

Note that ordinary, full template bandwidth events would not have been affected by this issue.

Background

Testing of @surabhi.sachdev's early warning events revealed that there were some ringing artifacts in the absolute value of the interpolated SNR time series. Normal events in O3 would not have been subject to this artifact because they have full-bandwidth SNR time series.

Here's a plot of the amplitude, phase, real, and imaginary parts of the SNR time series:

I studied a few different options for replacement interpolation strategies, and Catmull-Rom interpolation of amplitude and phase is the clear winner. See the following Jupyter notebooks:

• $105 for a demonstration of the ringing artifacts in the old interpolation scheme
• $109 for convergence tests on realistic simulated SNR time series

Example

Here is a localization of an early warning event prior to this patch (injected sky location shown as a white star):

And here is the same event after this patch: