Signal denoising based on adaptive fourier decomposition

Signal denoising based on the adaptive Fourier decomposition (AFD) is investigated and an approach, termed Jaya-based AFD combined with Savitzky-Golay filter, is offered to reconstruct the original signal under white Gaussian noise (WGN). Using the AFD, an analytic signal can be expressed via the summation of mono-components (MCs) whose energies are in decreasing order. Its ability to decompose signals according to their energy distributions makes the AFD useful for the signal reconstruction from noisy measurements with signal-to-noise ratios greater than zero in decibels. In every decomposition level, the conventional AFD requires an over-complete dictionary to determine the MCs. Without requiring such a dictionary, a metaheuristic optimization algorithm, termed Jaya, is used for determining the MCs. Savitzky-Golay filtering is then applied to the summation of MCs, which are obtained in every decomposition level of the noisy signal. Simulations performed on real-world signals show that the proposed approach provides satisfactory denoising performance.