Postprocessed time-delay interferometry for LISA

High-precision interpolation of LISA phase measurements allows signal reconstruction and formulation of time-delay interferometry (TDI) combinations to be conducted in postprocessing. The reconstruction is based on phase measurements made at approximately 10 Hz (for a 1 Hz signal bandwidth) at regular intervals independent of the TDI delay times. Interpolation introduces an error less than $1\times {10}^{-8}$ with continuous data segments as short as 2 s in duration. The 10 Hz sampling rate represents an increase from the 2 Hz sampling rate needed for the original implementation of TDI. The advantages of this technique include increased flexibility of the data analysis and significantly simplified hardware.

Figure 1

Sinc FIR filter kernel values (circles) with delay set to (a) $D=0$, and (b) $D=0.3$.

Figure 2

Comparison of interpolation error for four interpolation methods; truncated-sinc filter kernel, Blackman windowed-sinc filter kernel, ${\mathrm{\text{Blackman}}}^3$ windowed-sinc filter kernel, and Lagrange interpolation.

Figure 3

Amplitude spectral density of interpolation error for Lagrange filters, shown with the spectral density of the initial 2.5 Hz-bandlimited noise. Spectral density is estimated by a triangle-windowed, averaged periodogram.

Figure 4

Real-time TDI, in which the delays must be known at the time of measurement, and the TDI combinations are computed before transponding to Earth. TDI combination $X(t)$ shown [Eq. (8)].

Figure 5

Post-processed implementation of TDI combination $X(t)$.