Fractional Fourier-based denoising of kinematic signals with multiple impacts

This work is concerned with a novel denoising scheme based on repeated filtering in consecutive fractional Fourier transform domains. In particular, we leverage the effectiveness of a recently presented filter circuit for biomechanical signals into the case of kinematic signals with multiple impacts. The presented method generates a time-varying cutoff threshold that can accommodate the frequency expansions caused by the discrete non-stationarities present in the signal. This is achieved by means of a filter circuit which is composed of a small number of ordinary linear low-pass filters and appropriate fractional Fourier transforms. We show that the proposed method outperforms conventional low-pass filters in the quality of its output and its robustness against noise.