VMD Code Implementation: Variational Mode Decomposition Algorithm

Variational Mode Decomposition (VMD) represents a modern signal decomposition approach that utilizes a variational problem framework to break down signals into multiple intrinsic mode functions (IMFs). The core objective is to minimize the sum of estimated bandwidths for all extracted modes. As a non-parametric decomposition method, VMD requires no prior assumptions about signal morphology or frequency components, making it suitable for various signal processing applications. Compared to conventional decomposition techniques, VMD demonstrates superior adaptability and broader application domains. In VMD implementation, signal decomposition is achieved through solving variational optimization problems. This typically involves addressing a series of convex optimization subproblems, where each subproblem corresponds to estimating one specific mode. The algorithm implementation commonly includes key computational steps such as Hilbert transform for analytic signal generation, Wiener filtering for mode updating, and center frequency optimization through alternating direction method of multipliers (ADMM). A significant advantage of VMD lies in its capability to effectively decompose non-linear and non-stationary signals, making it particularly valuable for modern signal processing and data analysis applications. Furthermore, VMD finds practical implementations in data compression, signal denoising, image processing, and biomedical signal analysis, demonstrating both theoretical significance and practical utility across multiple engineering disciplines.