Multivariate intrinsic chirp mode decomposition

Abstract

A multivariate intrinsic chirp mode decomposition (MICMD) algorithm is proposed to process multivariate/multichannel signals. In contrast to most existing multivariate time-frequency decomposition techniques, the proposed MICMD can efficiently extract time-varying signals by solving a multivariate linear system. In this paper, we first define a multivariate intrinsic chirp mode (MICM) by assuming the presence of a joint or common instantaneous frequency (IF) among all channels. Then the IFs and instantaneous amplitudes (IAs) are modeled as Fourier series. IFs can be estimated using the framework of the general parameterized time-frequency transform and then the corresponding MICMs are reconstructed by solving multivariate linear equations through an extended least square method. MICMD can characterize a set of multivariate modes without requiring more user-defined parameters than the original ICMD. Its properties and advantages, including mode-alignment, computational complexity, filter bank structure, quasi-orthogonality, channel number and noise robustness, are investigated successively. MICMD outperforms both multivariate empirical mode decomposition (MEMD) and multivariate variational mode decomposition (MVMD) in extracting time-varying components. The computational complexity of the proposed MICMD is proven to be O(N), thus much faster than MNCMD, which is of O(N3) complexity. In the end, we highlight the utility and superiority of MICMD in three real-world cases, including the periodicity analysis in meteorology (three-channel), the α-rhythm separation in electroencephalogram (EEG) (four-channel), and the plant-wide oscillation detection in industrial control system (eleven-channel).