Estimation of the Second Derivative of Kinematic Impact Signals Using Fractional Fourier Domain Filtering

A new filtering algorithm is proposed for the accurate estimation of the second derivatives of kinematic signals with impacts. The algorithm operates in predetermined consecutive fractional Fourier transform domains and amounts to an overall linear low-pass filter with time-varying cutoff threshold, which can successfully accommodate the impact-induced changes in the frequency content of the signals. The proposed method was applied to experimentally acquired displacement data and the results have demonstrated its promising performance that was found superior to both conventional techniques and recently introduced advanced schemes.