The original data are time series of x and y coordinates which describe the displacement of an object or a subject on field. The data were collected with an semi automatic tracking system at 30 fps. After that it was applied a 6Hz Butterworth low pass filter.
Hi Pedro, There is no way of "not adding" noise when performing any operation using inputs carrying already noise in them (unless using 2 correlated inputs). In fact we are not "adding noise" as it already comes from the XY coordinates displacement data. If the 6Hz cut-off low-pass filter is not enough to remove the higher frequency noise of the displacement trajectories I would try a lower frequency cut-off.
If not feasible or if the result is not the desired one I would try, for instance, a 2D Savistky-Golay polynomial smoothing to the raw data (30Hz) prior to calculate the speed (actually you can apply directly the 1st derivative SG smoothing). I have the SG implemented in Excel (just need to find it).
Best, LG
The maximum velocity you believe could happen should guide you in choosing the cut-off frequency for the low-pass filter. Then is is just a simple problem of distance divided by time.
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