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 $O\left(N\right),$ thus much faster than MNCMD, which is of $O\left(N^3\right)$ 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 $\alpha$-rhythm separation in electroencephalogram (EEG) (four-channel), and the plant-wide oscillation detection in industrial control system (eleven-channel).

提出了一种多元固有线性调频模式分解（MICMD）算法来处理多元/多通道信号。与大多数现有的多元时频分解技术相比，所提出的MICMD通过求解多元线性系统可以有效地提取时变信号。在本文中，我们首先通过假设所有通道之间存在联合或共同的瞬时频率（IF）来定义多元固有线性调频模式（MICM）。然后，将IF和瞬时幅度（IA）建模为傅立叶级数。可以使用通用参数化时频变换的框架来估计IF，然后通过扩展最小二乘法求解多元线性方程，从而重构相应的MICM。MICMD可以表征一组多元模式，而不需要比原始ICMD更多的用户定义参数。依次研究了其特性和优点，包括模式对准，计算复杂度，滤波器组结构，准正交性，通道数和噪声鲁棒性。在提取时变分量时，MICMD的表现优于多元经验模式分解（MEMD）和多元变异模式分解（MVMD）。所提议的MICMD的计算复杂度被证明是 在提取时变分量时，MICMD的表现优于多元经验模式分解（MEMD）和多元变异模式分解（MVMD）。所提议的MICMD的计算复杂度被证明是 在提取时变分量时，MICMD的表现优于多元经验模式分解（MEMD）和多元变异模式分解（MVMD）。所提议的MICMD的计算复杂度被证明是$Ø（ñ），$ 因此比MNCMD快得多 $Ø（{ñ}^3）$复杂。最后，我们重点介绍了MICMD在三个实际案例中的实用性和优越性，包括气象学中的周期性分析（三通道），$\alpha$脑电图（EEG）的心律分离（四通道），以及工业控制系统中的全厂振动检测（十一通道）。