The rule of 1 s for padding kinematic data prior to digital filtering: Influence of sampling and filter cutoff frequencies

Abstract

The influence of signal sampling frequency and the low-pass digital filter cutoff frequency on the minimum number of padding points when applied to kinematic data are factors often absent in data processing descriptions. This investigation determined a relationship between the number of padding points and the ratio of filter cutoff to signal sampling frequencies ( f c/ f s). Two kinematic recordings were used which represented signals with high and low deterministic variation magnitudes at the signals’ beginning. Signal sampling rates (40–128 Hz) were generated at intervals of 1 Hz. Filter cutoff frequency was iterated from 2 to 10 Hz at 0.5 Hz intervals. Data extrapolation was performed using three different techniques (first order polynomial, third order polynomial, and data reflection). A maximum of 2 s of padding points were added to the beginning of each test signal which was then dual-pass filtered using a second order Butterworth filter. For each successive increase in the number of padding points, the filtered test signal was compared to a criterion signal and the root mean square difference (RMSD) over the first second was calculated. The number of padding points required to attain a constant RMSD was recorded as the minimum number of padding points needed for that ratio of filter cutoff to sampling frequency. As f c/ f s increased, the number of padding points decreased non-linearly. More padding points were required for the signal with higher deterministic variation at the beginning than the signal with lower deterministic variation. Additional padding points (beyond the determined minimum) did not further reduce the RMSD. The largest temporal extrapolation determined by the algorithm to produce a stable RMSD was 1 s. It is suggested that a minimum of 1 s of extraneous data be used when using a low-pass recursive digital filter to remove noise from kinematic data.