@Article{TintoDhurJosh:2021:MaReTi,
               author = "Tinto, Massimo and Dhurandhar, Sanjeev and Joshi, Prasanna",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Inter 
                         University Centre for Astronomy and Astrophysics} and {Max Planck 
                         Institute for Gravitational Physic}",
                title = "Matrix representation of time-delay interferometry",
              journal = "Physical Review D",
                 year = "2021",
               volume = "104",
               number = "4",
                pages = "e044033",
                month = "Aug.",
             keywords = "SPACE.",
             abstract = "Time-delay interferometry (TDI) is the 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 are removed at any time t and gravitational 
                         wave signals can be studied at a requisite level of precision. In 
                         this article we show the delay operators used in TDI can be 
                         represented as matrices acting on arrays associated with the laser 
                         noises and Doppler measurements. The matrix formulation is nothing 
                         but the group theoretic representation (ring homomorphism) of the 
                         earlier approach involving time-delay operators and so in 
                         principle is the same. It is shown that the homomorphism is valid 
                         generally and we cover all situations of interest. To understand 
                         the potential advantages the matrix representation brings, care 
                         must be taken by the data analyst to account for the light travel 
                         times when linearly relating the one-way Doppler measurements to 
                         the laser noises. This is especially important in view of the 
                         future gravitational wave projects envisaged. We show that the 
                         matrix formulation of TDI results in the cancellation of the laser 
                         noises at an arbitrary time t by only linearly combining a finite 
                         number of samples of the one-way Doppler data measured at and 
                         around time t.",
                  doi = "10.1103/PhysRevD.104.044033",
                  url = "http://dx.doi.org/10.1103/PhysRevD.104.044033",
                 issn = "1550-2368 and 1550-7998",
             language = "en",
           targetfile = "tinto_matrix.pdf",
        urlaccessdate = "29 jun. 2024"
}