OPTIMAL DIGITAL FILTERING REQUIRES A DIFFERENT CUTOFF FREQUENCY STRATEGY FOR THE DETERMINATION OF THE HIGHER DERIVATIVES

The present study investigated four different filtering and differenti ation sequences for the calculation of the higher derivatives from noi sy displacement data when using a second-order Butterworth filter and first-order finite differences. These were: (1) the conventional seque nce (i.e. filtering the displacement data and then differentiating); ( 2) filtering the displacement with a different cut-off frequency depen ding upon optimal 0th, 1st and 2nd derivatives; (3) double filtering a nd differentiation (only for acceleration); and (4) differentiation an d then filtering separately in each derivative domain, i.e. treating t he noisy higher derivatives as individual signals. Thirty levels of ti me domain and 30 levels of frequency domain computer-generated pure no ise signals, were superimposed oil 24 reference signals which simulate d the medial-lateral, anterior-posterior and vertical displacement pat terns of eight markers attached to the lower extremity segments during walking. The optimum cut-off frequency for the displacement, velocity and acceleration data was calculated as the one that produced the min imum root mean square error between the reference and noisy data in ea ch derivative domain. The results indicated that the conventional stra tegy has to be reconsidered and modified, as the best results were obt ained by the second strategy. The optimum cut-off frequency for accele ration was lower than that required for the velocity which in turn was lower than the optimum cut-off frequency for displacement. The findin gs of the present study will contribute to the development of existing and future automatic filtering techniques based on digital filtering. (C) 1997 Elsevier Science Ltd.