Nonlinear Chirp Mode Decomposition: A Variational Method

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 wideband 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. Our method can be viewed as a time–frequency 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.