IMF Computation Using EMD and Hilbert Transform with HHT Analysis

This paper presents a methodology that utilizes Empirical Mode Decomposition (EMD) and Hilbert Transform to compute Intrinsic Mode Functions (IMFs). The implementation involves key algorithmic steps: first applying EMD decomposition to extract IMF components from input signals, followed by Hilbert spectral analysis to generate three primary visualization outputs - the normalized Hilbert-Huang Transform (HHT) energy spectrum (displayed as a 3D plot), marginal spectrum diagram, and instantaneous energy distribution plot. The code architecture includes completeness validation routines that verify the decomposition's mathematical integrity by checking the reconstruction error between original signals and summed IMF components. This approach offers significant advantages over alternative methods through its simplified implementation workflow, utilizing core functions like emd() for decomposition and hilbert() for transform operations. The method's adaptability to various signal types and robust analytical capabilities suggest broad application potential across multiple signal processing domains, including biomedical engineering, mechanical fault diagnosis, and environmental data analysis. The program's effectiveness stems from its systematic processing chain: signal preprocessing, EMD iteration with stoppage criteria, Hilbert spectral computation, and energy normalization procedures. This structured methodology ensures reliable results while maintaining user-friendly operation suitable for both research and industrial applications.