Estimate of the Optimum Cutoff Frequency for the Butterworth Low-Pass Digital Filter

Abstract

The purposes of this study were (a) to develop a procedure for objectively determining the optimum cutoff frequency for the Butterworth low-pass digital filler, and (b) to evaluate the cutoff frequencies derived from the residual analysis. A set of knee flexion-extension angle data in normal gait was used as the standard data set. The standard data were sampled at different sampling frequencies. Random errors with different magnitudes were added to the standard data to create different sets of raw data with a given sampling frequency. Each raw data set was filtered through a Butterworth low-pass digital filter at different cutoff frequencies. The cutoff frequency corresponding to the minimum error in the second time derivatives for a given set of raw data was considered as the optimum for that set of raw data. A procedure for estimating the optimum cutoff frequency from the sampling frequency and estimated relative mean error in the raw data set was developed. The estimated optimum cutoff frequency significantly correlated to the true optimum cutoff frequency with a correlation determinant value of 0.96. This procedure was applied to estimate the optimum cutoff frequency for another set of kinematic data. The calculated accelerations of the filtered data essentially matched the measured acceleration curve. There is no correlation between the cutoff frequency derived from the residual analysis and the true optimum cutoff frequency. The cutoff frequencies derived from the residual analysis were significantly lower than the optimum, especially when the sampling frequency is high.