END-POINT ERROR IN SMOOTHING AND DIFFERENTIATING RAW KINEMATIC DATA -AN EVALUATION OF 4 POPULAR METHODS

'Endpoint error' describes the erratic behavior at the beginning and e nd of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpo int error produced by four popular smoothing and differentiating techn iques, Lanshammar's (1982, J. Biomechanics 15, 99-105) modification of the Pezzack er al. (1977, J. Biomechanics, 10, 377-382) raw angular d isplacement data set was truncated at three different locations corres ponding to the major peaks in the criterion acceleration curve. Also, for each data subset, three padding conditions were applied. Each data subset was smoothed and differentiated using the Butterworth digital filter, cubic spline, quintic spline, and Fourier series to obtain acc eleration values. RMS residual errors were calculated between the comp uted and criterion accelerations in the endpoint regions. Although no method completely eliminated endpoint error, the results demonstrated clear superiority of the quintic spline over the other three methods i n producing accurate acceleration values close to the endpoints of the modified Pezzack er al. (1977) data set. In fact, the quintic spline performed best with non-padded data (cumulative error = 48.0 rad s(-2) ). Conversely, when applied to non-padded data, the Butterworth digita l filter produced wildly deviating values beginning more than the 10 p oints from the terminal data point (cumulative error = 226.6 rad s(-2) ). Each of the four methods performed better when applied to data subs ets padded by linear extrapolation (average cumulative error = 68.8 ra d s(-2)) than when applied to analogous subsets padded by reflection ( average cumulative error = 86.1 rad s(-2)). Copyright (C) 1996 Elsevie r Science Ltd.