A movement amount detecting device performs discrete Fourier transform onto N-th image data and N+1-th image data, thereby generating N-th wave number space data and N+1-th wave number space data. The movement amount detecting device obtains a target speed of a sheet, and determines a cutoff value based on the obtained target speed and an exposure time in an image sensor. The movement amount detecting device calculates an amount of movement of the sheet based on a phase difference between the N-th wave number space data and the N+1-th wave number space data in a wave number component smaller than the cutoff value.