Filtering Eye-Tracking Data From an EyeLink 1000: Comparing Heuristic, Savitzky-Golay, IIR and FIR Digital Filters

TL;DR

The FIR filter had the sharpest roll-off of any filter and maintained the signal and removed noise more effectively than any other filter, and is recommended to be used.

Abstract

In a previous report (Raju et al.,2023) we concluded that, if the goal was to preserve events such as saccades, microsaccades, and smooth pursuit in eye-tracking recordings, data with sine wave frequencies less than 100 Hz (-3db) were the signal and data above 100 Hz were noise. We compare 5 filters in their ability to preserve signal and remove noise. Specifically, we compared the proprietary STD and EXTRA heuristic filters provided by our EyeLink 1000 (SR-Research, Ottawa, Canada), a Savitzky-Golay (SG) filter, an infinite impulse response (IIR) filter (low-pass Butterworth), and a finite impulse filter (FIR). For each of the non-heuristic filters, we systematically searched for optimal parameters. Both the IIR and the FIR filters were zero-phase filters. Mean frequency response profiles and amplitude spectra for all 5 filters are provided. In addition, we examined the effect of our filters on a noisy recording. Our FIR filter had the sharpest roll-off of any filter. Therefore, it maintained the signal and removed noise more effectively than any other filter. On this basis, we recommend the use of our FIR filter. Several reports have shown that filtering increased the temporal autocorrelation of a signal. To address this, the present filters were also evaluated in terms of autocorrelation (specifically the first 3 lags). Of all our filters, the STD filter introduced the least amount of autocorrelation.

Figures (5)

• Figure 1: Frequency response of all the filters (EyeLink heuristic filters and Digital filters). At -3dB signals are reduced by 50%, at -6dB signals are reduced by 75%, and so on as mentioned in the legend.
• Figure 2: Amplitude spectrum of the unfiltered signal and all of the filters evaluated in this report. Segments were chosen as described above.
• Figure 3: Effect of filtering on median temporal autocorrelation for unfiltered and filtered fixation segments.
• Figure 4: Analysis of autocorrelation results. Values plotted are Fisher Z transformed values from the original autocorrelations. Three box-plots that compare all filters. (A) Box-plots represent ACF lag 1. (B) Box-plots represent ACF lag 2. (C) Box-plots represent ACF lag 3.
• Figure 5: Illustration of the effect of filtering on positional signals and instantaneous velocity. A very noisy stretch of recording during our random saccade task was chosen. (A) Horizontal position signal, including a saccade of $\approx 1.25$ degrees of visual angle (dva) for a very noisy unfiltered recording and for filtered position signals of the same recording. Each of the filtered versions has an offset for better visualization. (B) Velocity (instantaneous) channel for the unfiltered data. (C) Velocity (instantaneous) channel of the filtered data. The IIR velocity channel was offset by 50 degrees per second (d/s) and the FIR velocity channel was offset by 100 d/s.