Padding point extrapolation techniques for the Butterworth digital filter.

Biomechanical studies of movement kinematics and kinetics often involve the measurement of analog quantities through discrete sampling of the signal at some regular interval. The digital data which result can, in most cases, adequately represent the original signal, providing the sampling frequency is high enough to respond to the high frequency components of that signal (Winter, 1979, p. 28). The ease of computer processing of digital data is a distinct advantage over analog data. However, in either case some signal conditioning is usually required before any quantitative analysis is performed. In the case of digital data, various smoothing routines have been developed for dealing with the random errors which are introduced in the measurement process. The most effective of these methods (spline functions, Fourier series and digital filters) have been described in detail elsewhere (see Wood, 1982 for a general review). The Buttenvorth digital filter is a recursive routine which uses prior data points (both smoothed and raw data) to predict subsequent smoothed data points (Gold and Rader, 1969). For biomechanical application, Winter (1979) suggested the use of a second order filter such as the following: