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I have data from an eye tracker collected while subjects were doing a saccadic task (i.e. fast eyes movements). Specifically, I have the position (in degree) on the x and y axes, collected at 120Hz.

My aim is to find the saccades relative to the fixations (i.e. point in time in which the eyes are relative fixed). This is generally done by finding some fixed or adapting velocity threshold.

Following what seems to be the consensus in the eye-tracking literature (e.g. this and this) I have calculated the velocity on the x and the y axes by applying a Savitzky–Golay filter to both the x-axis and the y-axis data, and calculating then the first derivative. Then, I have calculated the overall velocity by applying the formula $$ velocity = \sqrt{velocity_{x}^2 + velocity_{y}^2} $$

This approach seems to work overall, since there are indeed peaks in the velocity that are time locked with the saccades. However, I cannot apply the thresholds present in the literature for the automatic detection of the saccades, since my velocity values are on average much lower than those find in the literature (~75% lower).

I was wondering then if the problem could be the unit. All thresholds in literature are reported as degree/second, but I cannot understand what is the unit of the velocity I have calculated. Nowhere in the process I have entered information about the sampling frequency, so, to come back to the initial question: what is the unit of the velocity value I have calculated ?

fednem
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  • If your filtered or unfiltered data, $x(t)$ and $y(t)$, is position in degrees, then the associated time derivatives, $x'(t)$ and $y'(t)$, would be in degrees per second. The Savitzky-Golay filter is simply a localized low-order polynomial fit to smooth data. How are you calculating the derivative of the filtered data? – Ash Mar 02 '22 at 15:51
  • @Ash, I am using the `scipy.signal` implementation of the Savitzky-Golay filter `savgol` that allow to directly calculate the derivative after having fitted the filter. The point is that AFAIU the derivative should be in degrees per 'point' where point is one measure, since no information on the sampling frequency is provided. Shouldn't I be doing something more to convert to degree/second ? – fednem Mar 03 '22 at 09:23
  • Could you post some of your code? – Ash Mar 03 '22 at 15:55

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