A procedure for the automatic determination of filter cutoff frequency for the processing of biomechanical data

This article presents and evaluates a new procedure that automatically determines the cutoff frequency for the low-pass filtering of biomechanical data. The cutoff frequency was estimated by exploiting the properties of the autocorrelation function of white noise. The new procedure systematically varies the cutoff frequency of a Butterworth filter until the signal representing the difference between the filtered and unfiltered data is the best approximation to white noise as assessed using the autocorrelation function. The procedure was evaluated using signals generated from mathematical functions. Noise was added to these signals so that they approximated signals arising from the analysis of human movement. The optimal cutoff frequency was computed by finding the cutoff frequency that gave the smallest difference between the estimated and true signal values. The new procedure produced similar cutoff frequencies and root mean square differences to the optimal values, for the zeroth, first, and second derivatives of the signals. On the data sets investigated, this new procedure performed very similarly to the generalized cross-validated quintic spline.