When cosmic-ray arrival directions are observed in celestial coordinates, they appear to have a small anisotropy whose origin is still largely unknown. In addition to this celestial anisotropy, the Earth's revolution around the Sun produces a faint Compton-Getting dipole anisotropy with an excess oriented towards the direction of motion in solar coordinates. The relative rotation of the celestial and solar reference frames over a calendar year causes interference between the two sources of anisotropy. It is possible to characterize the resulting yearly modulations by studying the side-bands to the diurnal and sidereal frequencies in anti- and extended-sidereal time frames. This work provides a numerical simulation of the interference between anisotropies in sidereal and solar reference frames to predict the distributions in anti-sidereal and extended-sidereal frames.