Multivariate Jump Plus AM-FM Mode Decomposition (MJMD)

A novel method for decomposing a multivariate signal into AM-FM oscillations and discontinuous (jump)

Multivariate Jump Plus AM-FM Mode Decomposition (MJMD) is a novel method for decomposing a multivariate signal into amplitude- and frequency-modulated (AM-FM) oscillations and discontinuous (jump) components. Current multivariate signal decomposition methods are designed to either obtain constituent AM-FM oscillatory modes from the data. Yet, many real-world signals of interest simultaneously exhibit both behaviors i.e., jumps and oscillations. In MJMD method, we design and solve a variational optimization problem to accomplish this task. The optimization formulation includes a regularization term to minimize the bandwidth of all signal modes for effective oscillation modeling, and a prior for extracting the jump component. MJMD addresses the limitations of conventional AM-FM signal decomposition methods in extracting jumps, as well as the limitations of existing jump extraction methods in decomposing multiscale oscillations.