An object moving in discrete spatial jumps is difficult to distinguish from a continuously moving object, provided the time between jumps is not too great. The extent of this perceived continuity may be measured by probing the perceived spatial location at times between the target jumps, by either a vernier alignment or a stereoscopic technique. As the time between jumps increases the accuracy of spatial interpolation falls, until finally the object is seen only at its actual spatial locations. These results can be analysed in the frequency domain by treating the signal for apparent motion as the analogue of a periodic waveform containing relatively low frequencies (the continuous motion) and higher frequencies giving rise to the discreteness of the motion. If such an input has the higher frequencies progressively removed by physical filtering, it is perceived as increasingly continuous. The fact that such filtering is not necessary for perceived continuity when the discrete jumps occur at rates greater than about 30 Hz suggests that frequencies greater than that limit are removed by the visual system itself.