variational nonlinear chirp mode decomposition

Method for decompose nonlinear chirps with multiple signal modes

Variational mode decomposition (VMD), a recently introduced method for adaptive data analysis, has aroused much attention in various fields. However, the VMD is formulated based on the assumption of narrow-band property of the signal model. To analyze wide-band nonlinear chirp signals (NCSs), we present an alternative method called variational nonlinear chirp mode decomposition (VNCMD). The VNCMD is developed from the fact that a wide-band NCS can be transformed to a narrow-band signal by using demodulation techniques. Our decomposition problem is thus formulated as an optimal demodulation problem which is efficiently solved by the alternating direction method of multipliers (ADMM). Our method can be viewed as a time-frequency (TF) filter bank which concurrently extracts all the signal modes. Some simulated and real data examples are provided showing the effectiveness of the VNCMD in analyzing NCSs containing close or even crossed modes.
The matlab codes permit to reproduce some results in the paper: Chen S, Dong X, Peng Z, et al, Nonlinear Chirp Mode Decomposition: A Variational Method, IEEE Transactions on Signal Processing, 2017. Some of the scripts and examples are adopted from the paper: S. Chen, Z. Peng, Y. Yang, et al, Intrinsic chirp component decomposition by using Fourier Series representation, Signal Processing, 2017, 137: 319-327. and the paper: Chen S, Dong X, Xing G, et al, Separation of Overlapped Non-Stationary Signals by Ridge Path Regrouping and Intrinsic Chirp Component Decomposition, IEEE Sensors Journal, 2017.
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