Spline solution to terminal zero acceleration problems in biomechanical data

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Abstract
An augmented cubic spline function was evaluated as an alternative solution to the end-point problem which frequently arises in the smoothing and differentiation of [human] biomechanical position-time data. The usual procedures of natural cubic spline functions and digital filtering have the undesirable effect of forcing the accelerations to zero at the ends of the data set. The proposed augmented cubic spline procedure does not have this characteristic but rather requires the curve to pass through a single extra point at each end of the data set. Using 2 different criteria with large acceleration magnitudes near the end of the data set, the effectiveness of all 3 methods was compared in terms of the total curve (root mean square error) and in terms of the last few points (percent and algebraic error). In both experiments the augmented cubic spline procedure was superior to both digital filtering and natural cubic spline functions. This technique could be used for smoothing and differentiating biomechanical data in instances where the underlying function is unknown and the accelerations at the end points of the data set are suspected of being non-zero.

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