Resampled random processes in gravitational-wave data analysis

The detection of continuous gravitational-wave signals requires to account for 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 needs to be transformed from the topocentric time to the barycentric time by means of resampling. The resampled data form a non-stationary random process. In this communication we prove that this non-stationary random process is mathematically well defined, and show that generalizations of the fundamental results for stationary processes, like Wiener-Khintchine theorem and Cram\`{e}r representation, exist.