Variational Mode Decomposition (VMD)

Variational Mode Decomposition (VMD) provides an effective method for processing nonlinear and non-stationary signals. Compared to traditional Empirical Mode Decomposition (EMD), VMD offers several advantages and addresses certain limitations inherent in the EMD approach. The implementation typically involves solving a constrained variational optimization problem to decompose signals into intrinsic mode functions with specific sparsity properties. Algorithm key components include Wiener filtering in the Fourier domain and Hilbert transform for frequency domain analysis. This package includes complete MATLAB/Python implementation code demonstrating the VMD algorithm workflow: signal preprocessing, mode extraction parameters (number of modes, balancing parameter), and reconstruction error analysis. The accompanying technical paper details the mathematical foundation, convergence properties, and practical applications across various signal processing domains.