Automatic segment filtering procedure for processing non-stationary signals

Computing time derivatives is a frequent stage in the processing of biomechanical data. Unfortunately, differentiation amplifies the high frequency noise inherent within the signal hampering the accuracy of signal derivatives. A low-pass Butterworth filter is commonly used to reduce the sampled signal noise prior to differentiation. One hurdle lies in selecting an appropriate filter cut-off frequency which retains the signal of interest while reducing deleterious noise. Most biomechanics data processing approaches utilize the same cut-off frequency for the whole sampled signal, but the frequency components of a signal can vary with time. To accommodate such signals, the Automatic Segment Filtering Procedure (ASFP) is proposed which uses different automatically determined Butterworth filter cut-off frequencies for separate segments of a sampled signal. The Teager-Kaiser Energy Operator of the signal is computed and used to determine segments of the signal with different energy content. The Autocorrelation-Based Procedure (ABP) is used on each of these segments to determine filter cut-off frequencies. This new procedure was evaluated by estimating acceleration values from the test data set of Dowling (1985). The ASFP produced a root mean square error (RMSE) of 16.4 rad s⁻² (26.6%) whereas a single ABP determined filter cut-off frequency applied to the whole Dowling (1985) signal, representing the common approach, produced a RMSE of 25.5 rad s⁻² (41.4%). As a point of comparison, a Generalized Cross-Validated Quintic Spline, a common non-Butterworth filter, produced a RMSE of 23.6 rad s⁻² (38.4%). This new automatic approach is advantageous in biomechanics for preserving high frequency content of non-stationary signals.