Determining Which Sine Wave Frequencies Correspond to Signal and Which Correspond to Noise in Eye-Tracking Time-Series


The Fourier theorem proposes 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 of these frequencies are important to reproduce key qualities of eye-movements (``signal'') and some of these frequencies are not important (``noise''). We looked at three types of analysis: (1) visual inspection of plots of saccade, microsaccade and smooth pursuit exemplars; (2) an analysis of the percentage of variance accounted for (PVAF) in each of 1,033 unfiltered saccade trajectories by each frequency cutoff; (3) an analysis of saccade peak velocity in the unfiltered and various filtered conditions. Visual inspection suggested that frequencies up to 75 Hz are required to represent microsaccades. Our PVAF analysis indicated that data in the 0-25 Hz band are sufficient to account for nearly 100% of the variance in unfiltered saccade trajectories. Our analysis indicated that frequencies below 100 Hz are sufficient to maintain peak velocities. Therefore, our overall conclusion is that to maintain eye-movement signal and reduce noise, a cutoff frequency of 100 Hz is appropriate. Our results have implications for the proposed sampling rate of eye-tracking recordings. If one is working in the frequency domain and 100 Hz needs to be preserved, the minimum required sampling rate would be 200 Hz. However, in a time domain analysis, a minimum 1000 Hz sampling rate is required.


There are 1,033 saccade signals. The actual saccade starts at sample 211 and ends at 201 samples before the end of the signal vector.


eye tracking, signal, noise, fourier, Computer Science



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