Adaptive Fourier Decomposition for Multi-Channel Signal Analysis

Evolved from the conventional Fourier decomposition based on a pre-defined basis, Adaptive Fourier decomposition (AFD) uses adaptive basis to achieve the fast energy convergence. This paper extends the AFD to the multi-channel case, which finds common adaptive basis across all channels. The proposed multi-channel AFD (MAFD) scheme includes the multi-channel core AFD for general signals and the multi-channel unwinding AFD for specific signals that have common inner functions. Owing to the merits of the original AFD, the MAFD can provide sparse joint time-frequency distribution by computing the transient time frequency distribution (TTFD) across channels. Simulations on synthetic and real-world signals demonstrate that the proposed scheme can find and apply the common adaptive basis with desired properties maintained by the AFD, showing high potentials in real-world applications.