Rmd: Robust Modal Decomposition with Constrained Bandwidth

Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods are generally classified into two categories: numerical optimization-based methods (EMD, VMD) and spectral decomposition methods (SSA) that consider the physical meaning of signals. The former can produce spurious modes due to the lack of physical constraints, while the latter is more sensitive to noise and struggles with nonlinear signals. Despite continuous improvements in these methods, a modal decomposition approach that effectively combines the strengths of both categories remains elusive. This paper thus proposes a Robust Modal Decomposition (RMD) method with constrained bandwidth, which preserves the intrinsic structure of the signal by mapping the time series into its trajectory-GRAM matrix in phase space. Moreover, the method incorporates bandwidth constraints during the decomposition process, enhancing noise resistance. Extensive experiments on synthetic and real-world datasets, including millimeter-wave radar echoes, electrocardiogram (ECG), phonocardiogram (PCG), and bearing fault detection data, demonstrate the method's effectiveness and versatility. All code and dataset samples are available on GitHub: https://github.com/Einstein-sworder/RMD.