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We present a theoretical approach to study the effect of microwave radiation on the magnetoresistance of a one-dimensional superlattice. In our proposal the magnetoresistance of a unidirectional spatial periodic potential (superlattice), is modulated by microwave radiation due to an interference effect between both space-and time-dependent potentials. The final magnetoresistance will mainly depend on the spatial period of the superlattice and the radiation frequency. We consider an approach to study these effects based on the fast Fourier transform of the obtained magnetoresistance profiles in function of the inverse of the magnetic field. Based on this theory we propose the design of a novel radiation sensor for the terahertz band. Copyright (C) EPLA, 2015.