**Technical Note: Journal of Biomechanics 30(8), 851-855 **

Optimal Digital Filtering Requires a Different Cut-off Frequency Strategy for the Determination of the Higher Derivatives

by

Giannis Giakas and Vasilios Baltzopoulos

**Abstract**

The present study investigated four different filtering and differentiation sequences for the calculation of the higher derivatives from noisy displacement data when using a second order Butterworth filter and first order finite differences. These were: 1) the conventional sequence (i.e. filtering the displacement data and then differentiating); 2) filtering the displacement with a different cut-off frequency depending upon optimal 0th, 1st and 2nd derivatives; 3) double filtering and differentiation (only for acceleration); and 4) differentiation and then filtering separately in each derivative domain i.e. treating the noisy higher derivatives as individual signals. Thirty levels of time domain and 30 levels of frequency domain computer generated noisy signals, were superimposed on 24 reference signals which simulated the medial-lateral, anterior-posterior and vertical displacement patterns of eight markers attached to the lower extremity segments during walking. The optimum cutoff frequency for the displacement, velocity and acceleration data was calculated as the one that produced the minimum root mean square error between the reference and noisy data in each derivative domain. The results indicated that the conventional strategy has to be reconsidered and modified as the best results were obtained by the second strategy. The optimum cut-off frequency for acceleration was lower than that required for the velocity which in turn was lower than the optimum cut-off frequency for displacement. The findings of the present study will contribute to the development of existing and future automatic filtering techniques based on digital filtering.

**Technical Note: Journal of Biomechanics 30(8), 847-850 **

A comparison of automatic filtering techniques applied to biomechanical walking data

by

Giannis Giakas and Vasilios Baltzopoulos

**Abstract **

The purpose of this study was to compare and evaluate six automatic filtering techniques commonly used in biomechanics for filtering gait analysis kinematic signals; namely: 1) Power spectrum (signal-to-noise ratio) assessment; 2) Generalised cross validation spline; 3) Least squares cubic splines; 4) Regularisation of Fourier series; 5) Regression model and 6) Residual analysis. A battery of 1440 signals representing the displacements of seven markers attached upon the surface of the right lower limbs and one marker attached upon the surface of the sacrum during walking were used; their original signal and added noise characteristics were known a priori. The signals were filtered with every technique and the root mean square error between the filtered and reference signal was calculated for each derivative domain. Results indicated that among the investigated techniques there is no one that performs best in all the cases studied. Generally, the techniques of power spectrum estimation, least squares cubic splines and generalised cross validation produced the most acceptable results.