VMD Source Code: Variational Mode Decomposition Algorithm Implementation

Variational Mode Decomposition (VMD) is a nonlinear signal analysis technique that decomposes a signal into multiple intrinsic mode functions (IMFs) with specific center frequencies. The core algorithm iteratively determines these IMFs by solving a variational optimization problem that minimizes the sum of bandwidths of all modes while maintaining reconstruction fidelity. These IMF components can then be summed to reconstruct the original signal. The VMD implementation typically involves several key computational steps: frequency domain initialization, Wiener filtering updates for each mode, and center frequency optimization using Hilbert transforms. The algorithm employs alternating direction method of multipliers (ADMM) to efficiently solve the constrained variational problem. Originally developed for signal processing applications, VMD has found extensive applications across various domains including finance (market trend analysis), medical engineering (biomedical signal processing), and astronomy (celestial signal analysis). VMD demonstrates particular effectiveness in handling non-stationary and nonlinear signals, making it a powerful tool for modern signal analysis. To implement VMD signal decomposition, the core algorithm requires parameter configuration including the number of decomposition modes (K), balancing parameter (alpha), and convergence tolerance. The implementation typically involves frequency domain operations and iterative optimization loops. The VMD decomposition helps researchers understand the frequency composition of complex signals and how these components combine to form the original waveform. Additionally, VMD facilitates identification and separation of outliers or noise components within signals, enabling effective noise reduction and anomaly detection through selective IMF reconstruction.