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Transformation of the Spectrum of a Signal in Communication between Relativistically Moving Inertial Frames

Future space exploration may involve communications between spacecraft moving at relativistic velocities. One of the significant problems associated with such communication is spectral distortion of signals which are propagated between relativistic frames. This distortion is generated by both changing propagation distances and purely relativistic electromagnetic field transformations. In this paper a linear integral transformation is formulated for relating the Fourier spectra of the source antenna excitation current and the resulting incident electric field at the receiving antenna. The kernel of the transformation is evaluated for the case of a steerable source antenna tracking on the advanced receiver position. The transformation is then applied to the case of an ideal thin-wire half-wave dipole source antenna excited by a narrowband, double-sideband modulated current. The specific distortions of spectral spreading and translation are then related to increased bandwidth and upper cutoff frequency requirements of receiving systems in relativistic applications.