How to unconfound the directional and orientational information in visual neuron's response

When drifting bars or gratings are used as visual stimuli, information about orientation specificity (which has a period of 180 degrees) and direction specificity (which has a period of 360 degrees) is inherently confounded in the response of visual cortical neurons, which have long been known to be selective for both the orientation of the stimulus and the direction of its movement. It is essential to "unconfound" or separate these two components of the response as they may respectively contribute to form and motion perception, two of the main streams of information processing in the mammalian brain. Wörgötter and Eysel (1987) recently proposed the Fourier transform technique as a method of unconfounding the two components, but their analysis was incomplete. Here we formally develop the mathematical tools for this method to calculate the peak angles, bandwidths, and relative strengths, the three most important elements of a tuning curve, of both the orientational and the directional components, based on the experimentally-recorded neuron's response polar-plot. It will be shown that, in the 1-D Fourier decomposition of the polar-plot along its angular dimension, 1) the odd harmonics contain only the directional component, while the even harmonics are contributed to by both the orientational and the directional components; 2) the phases and the amplitudes of all the harmonics are related, respectively, to the peak angle and the bandwidth of the individual component. The basic assumption used here is that the two components are linearly additive; this in turn is immediately testable by the method itself.