Smoothing and differentiation of displacement-time data: an application of splines and digital filtering

The advent of the digital computer has allowed workers in the field of biomechanics to perform data smoothing and time differentiation numerically. The methods which are most commonly used are spline functions and digital filtering. This paper provides raw displacement-time data for an object falling in the earth's gravitational field and demonstrates the results obtained using splines and digital filtering to calculate acceleration. It is recommended that the quintic spline is a good method to use provided one has sufficient core available, and the digital filter, with some form of augmentation and/or velocity smoothing, can yield satisfactory results for the user who has a mini- or micro-computer. Listings of the digital filter and finite difference subroutines are provided.