Implementation of IMF Extraction Using EMD and Hilbert Transform

This implementation utilizes Empirical Mode Decomposition (EMD) and Hilbert Transform to perform Hilbert-Huang Transform (HHT), generating normalized energy spectrum (3D visualization), marginal spectrum, and instantaneous energy diagrams. The process includes completeness verification to ensure computational accuracy and result reliability. The algorithm workflow comprises: 1. EMD decomposition to extract Intrinsic Mode Functions (IMFs) from input signals 2. Hilbert spectral analysis applied to each IMF component 3. Energy distribution calculation across time-frequency domains 4. Three-dimensional visualization of normalized energy spectrum 5. Marginal spectrum integration over frequency domains 6. Instantaneous energy tracking through time evolution 7. Completeness validation comparing original and reconstructed signals Key implementation aspects: - EMD algorithm handles non-stationary signal decomposition through sifting processes - Hilbert transform produces analytic signals for instantaneous frequency calculation - Energy normalization ensures comparable scales across different signal components - Visualization functions plot 3D energy distributions with time-frequency coordinates - Validation routines verify signal reconstruction accuracy from IMF components