Generalized Variational Mode Decomposition: A Multiscale and Fixed-Frequency Decomposition Algorithm

To overcome the limitations of variational mode decomposition (VMD) algorithm that its frequency scales and spectrum positions cannot be flexibly adjusted to decompose signals as required, a generalized VMD (GVMD) was proposed. This article addresses the fundamental theory of GVMD. In order to highlight the local characteristics of the signal much more while considering its global data fidelity, a set of variational models is formed, where individual constrained optimization problem is constructed for each mode. The formed variational models are solved by the modified alternating direction method of multipliers approach, thus realizing the multiscale and fixed-frequency decomposition. To gain a deep insight into GVMD algorithm, its frequency band division manner is investigated. In essence, GVMD can be viewed as a bank of filters whose bandwidths and center frequencies can be flexibly adjusted by its parameters, i.e., scale parameters and prior center frequencies. The effectiveness of GVMD is verified on simulated and real signals. The preliminary results show that compared with state-of-the-art methods, GVMD can make full use of feature information to decompose original signals as desired into several narrowband modes or into several narrowband modes and a wideband mode, effectively obtaining the interested modes.