Investigate differentiation and integration
In the current implementation differentiation is done by centered finite difference (
numpy.gradient) and integration by a cumulative trapezoidal sum (
scipy.integrate.cumulative_trapezoid). Those operations are not exact but the error decreases for small frequencies. We need to investigate how exact they are in the LISA band and whether we have to increase accuracy by increasing the order of the specific operation.
Another aspect of differentiation and integration is that they should be the inverse of each other, i.e. successive application should be equivalent to unity. I set up a simple experiment to check how 'unity' it gets with the current choice:
At the moment that might be enough but we need to be careful in the future about how this impacts the L0 data (also in the context of decimation). For example, the sideband measurement that track the derivative of the MPRs with high accuracy are slightly inconsistent with the MPRs coming from the PRN scheme.