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The present contribution is concerned with obtaining plane-wave spectral representations of the relativistic electric and magnetic dyadic Green's functions of an isotropic dielectric-magnetic medium (at the frame-at-rest) that is moving in a uniform velocity. By applying a simple coordinate transformation, scalarization of the EM vectorial problem is obtained in which the EM dyads are evaluated from Helmholtz's isotropic scalar Green's function. The spectral plane-wave representations of the dyadic Green's functions are obtained by applying the spatial 2D Fourier transform to the scalar Green's function. We investigate these spectral representations in the under and over phase-speed regimes, as well as 2D and 3D formulations and discuss the associated wave phenomena.