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While studying the responses of the oculomotor system to horizontally moving visual stimuli some interesting learning patterns were observed. Responses to Gaussian random noise, sine, and square-wave inputs were investigated. Based on small-signal, linear analysis, the system's transfer function was computed on the basis of both sinusoidal and random inputs. Assuming unity feedback, the open-loop transfer function was also computed for both of the above inputs. It is shown that the anticipatory behaviors observed during the tracking of periodic inputs, can be attributed to a prediction operator. This operator is determined by comparing the open-loop transfer functions for both stimuli. It is shown that the effect of this operator is a significant increase in low-frequency gain, and considerable phase-lead; monotonically increasing with frequency.