Time-delay interferometry (TDI) is a data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite linear combinations of properly time-shifted Doppler measurements, laser phase fluctuations can be removed at any time $t$ and gravitational wave signals can be studied at the requisite level of sensitivity. In the past, other approaches to this problem have been proposed. Recently, matrix-based approaches have been put forward; two such approaches are by Vallisneri et al. and Tinto et al. In this paper, we establish a close relationship between these approaches. In fact, we show that the matrices involved in defining the operators in the two approaches exhibit an isomorphism, and therefore, in both approaches one is dealing with matrix representations of the time-delay operators.

• Received 2 December 2021
• Accepted 5 April 2022

DOI:https://doi.org/10.1103/PhysRevD.105.084063

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society