Variational Mode Decomposition (VMD)

This text introduces Variational Mode Decomposition (VMD), an advanced signal processing technique that reformulates signal decomposition as a constrained variational optimization problem. The method autonomously decomposes complex signals into sums of multiple Intrinsic Mode Functions (IMFs) through an iterative optimization process involving Wiener filtering and Hilbert transform operations. In implementation, VMD employs Lagrange multipliers and quadratic penalty terms to enforce bandwidth constraints, typically coded using optimization algorithms like alternating direction method of multipliers (ADMM). The decomposition process involves key parameters including the number of modes K, bandwidth control parameter α, and convergence tolerance τ, which collectively determine the spectral separation precision. This technique proves particularly valuable in non-stationary signal analysis, enabling detailed examination of signal characteristics and dynamic variations through well-defined frequency-band limited IMF components. Consequently, VMD serves as a powerful computational tool for applications requiring high-resolution time-frequency analysis and component separation in signal processing research.