On practical evaluation of differentiation techniques for human gait analysis.

Numerical differentiation of noisy measurement data represents a problem frequently encountered in the field of gait analysis. There are two major determinants of the quality in calculated derivatives, namely the quality of the measurement data and the quality of the used differentiation technique. The quality of the measurement data, with respect to the maximum precision that can be obtained in calculated derivatives, is discussed with the help of an error formula valid for all differentiating techniques. It is verified that high precision can be obtained in the calculated second derivatives even with crude techniques, provided that the quality of the measurement data are good enough. This point is illustrated by the differentiation film data from Pezzack et al. (1977), using a least squares polynomial fitting. For the evaluation and comparison of different techniques for numerical differentiation it is recommended that measurement data with a considerable amount of noise is used, and that the quality of calculated derivatives are evaluated not only by visual inspection of graphical displays, but also with the use of a quantitative criteria, such as the root mean squares error.