Successive Nonlinear Chirp Component Analysis

Nonlinear Component Chirp Analysis (NCCA) is designed to extract non-stationary source signals and mixing vectors from instantaneous linear mixing model, which is commonplace in blind source separation (BSS) problems. However, several challenges limit its practical application: (i) the number of source signals must be predetermined; (ii) computation time increases significantly with the number of source signals; and (iii) the bandwidth parameter remains fixed throughout the entire process. To address these issues, this paper proposes Successive NCCA. In this approach, source signals are treated as Nonlinear Chirp Modes (NCMs) and are sequentially captured by Successive NCCA in a recursive framework, continuing until the energy ratio of the residual signal falls below a set threshold. This method eliminates the need to predetermine the number of source signals and significantly reduces computation time. Additionally, the Index of Orthogonality (IO) between the source signal and the residual signal is used to adaptively adjust the bandwidth parameter. A series of synthetic signals is employed to evaluate the performance of Successive NCCA, including its mode alignment capability, underdetermined blind source separation (UBSS) ability, filter-bank structure, computational efficiency, and convergence properties. Finally, Successive NCCA is applied to the separation of $\alpha$-rhythms in multichannel electroencephalogram (EEG) data and the analysis of time-varying vibration systems.