Validate post-response twisting-up for slowly precessing LISA sources

Investigate whether the twisting-up procedure can be applied after time-delay-interferometry and Wilson-Daubechies-Meyer transformation for slowly precessing systems when the precession rotation varies little across the relevant delays and wavelet support.

Background

The paper discusses reusing sparse time-delay-interferometry and Wilson-Daubechies-Meyer transforms by separating waveform shape parameters from projection parameters. For precessing sources, constant source-orientation rotations may be treated as projection parameters, but the time-dependent precession rotation generally does not commute with the time-delay-interferometry delays or act pointwise on Wilson-Daubechies-Meyer coefficients.

The authors suggest that slowly precessing systems may admit a computationally useful approximation in which the twisting-up operation is performed after the detector response and time-frequency transformation. The validity and accuracy of this post-response approximation remain unresolved, particularly when assessed across the relevant detector delays and wavelet support.