Resampled random processes in gravitational-wave data analysis

The detection of continuous gravitational-wave signals requires taking into account the motion of the detector with respect to the solar system barycenter in the data analysis. In order to search efficiently for such signals by means of the fast Fourier transform the data need to be transformed from the topocentric time to the barycentric time by means of resampling. The resampled data form a nonstationary random process. In this Brief Report we prove that this nonstationary random process is mathematically well defined, and show that generalizations of the fundamental results for stationary processes, such as the Wiener-Khintchine theorem and Cramèr representation, exist.