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

arXiv: https://arxiv.org/abs/2302.00029 · HTML: https://mlsanity.com/paper/2302.00029/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2023.

## Built on by (most cited first, 2 of 2)

- [Temporal Persistence and Intercorrelation of Embeddings Learned by an End-to-End Deep Learning Eye Movement-driven Biometrics Pipeline](https://mlsanity.com/paper/2402.16399/) (2024)
- [EyeMakeYou: Identity-, Task-, and Subjective-State-Conditioned Diffusion for High-Frequency Gaze Synthesis](https://mlsanity.com/paper/2609.04501/) (2026)

## Abstract (arXiv)

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.