This paper addresses the problem to extract moving object from the moving background in the mixed domain (MixeD), which makes it possible to carry the filtering in one dimension. Since the velocities of moving object and background are necessary for moving object extraction, we first estimate the velocities based on the appropriate spatial frequency point selection method in the MixeD. Then an optimal filter used for 1-D signal filtering is designed. By filtering 1-D signals over all spatial frequencies, signals with certain velocity vector are extracted, while the extracted image is obtained by applying the 2-D IDFT to the filtered signals. The simulation results show that the method can extract moving object based both on the correctly estimated velocity and the proposed optimal 1-D filter.