Fourier components of moving gratings

In designing experiments in which the proximal stimulus is a moving grating (including cases in which the distal stimulus is stationary but eye movements play a significant role), one must consider the effects of the motion of the stimulus on its Fourier components in the spatiotemporal frequency domain. Some of these effects are unexpected and counterintuitive. For example, the Fourier components of a moving grating do not include its stationary (or “instantaneous”) spatial frequency. Thus there is no linear filter that can extract a stationary grating from a moving one. Several useful relations are given for analyzing such stimuli.