The interaction of light with objects and media moving at relativistic and superluminal speeds enables unconventional phenomena such as Fresnel drag, Hawking radiation, and light amplification. Synthetic motion, facilitated by modulated internal degrees of freedom, enables the study of relativistic phenomena unrestricted by the speed of light. In this study, we investigate synthetically moving apertures created by high-contrast reflectivity modulations, which are generated by ultrafast laser pulses on a subwavelength thin film of indium tin oxide. The space-time diffraction of a weaker probe beam reveals a complex, non-separable spatio-temporal transformation, where changes in the frequency of the wave are correlated to changes in its momentum. By using schemes of continuous or discrete modulation we demonstrate tunable frequency-momentum diffraction patterns with gradients that depend upon the relative velocity between the modulation and the probe wave. The diffraction patterns are matched by operator-based theory and the gradients are analytically predicted using a super-relativistic Doppler model, where the modulation is described as a superluminally moving scattering particle. Our experiments open a path towards mimicking relativistic mechanics and developing complex and programmable spatio-temporal transformations of light.