A blind source separation method: Nonlinear chirp component analysis.

In this paper, a novel blind source separation (BSS) method drawing on the framework of Multivariate nonlinear chirp mode decomposition (MNCMD) termed as Nonlinear Chirp Component Analysis (NCCA) is proposed. In contrast to other BSS methods, NCCA is designed to separate the non-stationary sources in an elegant variational optimization framework. Firstly, the source signals are modeled as wide-band nonlinear chirp modes (NCMs) which could be transformed into narrow-band signals with demodulation techniques. Afterwards, the objective function is represented as the summation of source signals bandwidths fulfilling the constraint that the multivariate observed signal is the linear combination of the source signals. Finally, the alternate direction method of multipliers (ADMM) algorithm is employed to solve this optimization problem without more predefined parameters than MNCMD. After that, the source signals including their instantaneous frequency (IF), instantaneous amplitude (IA), the mixing matrix are updated to the optimal values. The merits of NCCA inherited from MNCMD like mode-aligned, filter bank structure, Quasi-orthogonality of modes and its unique attribute of identifying the BSS model and undetermined blind source separation (UBSS) model are testified through a series of synthetic signal. Its anti-noise property and convergence property get verified too. The performance of NCCA in the analysis of vibration analysis through simulation and experimental vibration system is highlighted in the end. [ABSTRACT FROM AUTHOR]