  The Fourier theorem states that any time-series can be decomposed into a set
of sinusoidal frequencies, each with its own phase and amplitude. The
literature suggests that some frequencies are important to reproduce key
qualities of eye-movements ("signal") and some of frequencies are not important
("noise"). To investigate what is signal and what is noise, we analyzed our
dataset in three ways: (1) visual inspection of plots of saccade, microsaccade
and smooth pursuit exemplars; (2) analysis of the percentage of variance
accounted for (PVAF) in 1,033 unfiltered saccade trajectories by each frequency
band; (3) analyzing the main sequence relationship between saccade peak
velocity and amplitude, based on a power law fit. Visual inspection suggested
that frequencies up to 75 Hz are required to represent microsaccades. Our PVAF
analysis indicated that signals in the 0-25 Hz band account for nearly 100% of
the variance in saccade trajectories. Power law coefficients (a, b) return to
unfiltered levels for signals low-pass filtered at 75 Hz or higher. We conclude
that to maintain eye movement signal and reduce noise, a cutoff frequency of 75
Hz is appropriate. We explain why, given this finding, a minimum sampling rate
of 750 Hz is suggested.
