Estimate of the optimum cutoff frequency for the Butterworth low-pass digital filter

The purposes of this study were (a) to develop a procedure for objectively determining the optimum cutoff frequency for the Butterworth low-pass digit al filter, and (b) to evaluate the cutoff frequencies derived from the resi dual analysis. A set of knee flexion-extension angle data in normal gait wa s used as the standard data set. The standard data were sampled at differen t sampling frequencies. Random errors with different magnitudes were added to the standard data to create different sets of raw data with a given samp ling frequency. Each raw data set was filtered through a Butterworth low-pa ss digital filter at different cutoff frequencies. The cutoff frequency cor responding 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 p rocedure for estimating the optimum cutoff frequency from the sampling freq uency 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. Thi s procedure was applied to estimate the optimum cutoff frequency for anothe r set of kinematic data. The calculated accelerations of the filtered data essentially matched the measured acceleration curve. There is no correlatio n between the cutoff frequency derived from the residual analysis and the t rue optimum cutoff frequency. The cutoff frequencies derived from the resid ual analysis were significantly lower than the optimum, especially when the sampling frequency is high.