Hilbert Huang Transform: Algorithm Fundamentals and Implementation Approaches

This article explores the fundamental concepts of Hilbert Huang Transform (HHT) and its extensive applications in signal processing and analysis. HHT operates as an adaptive local characteristic-based analytical method that decomposes nonlinear and non-stationary signals into Intrinsic Mode Functions (IMFs) and residual components. The core algorithm involves two key stages: empirical mode decomposition (EMD) for IMF extraction and Hilbert spectral analysis for instantaneous frequency calculation. IMFs represent functions exhibiting monotonicity and self-similarity properties, enabling extraction of periodic and trend components from signals to reveal inherent structures and dynamic characteristics. The EMD implementation typically utilizes iterative sifting processes with envelope detection algorithms, while the Hilbert transform stage employs convolution operations with 1/t kernels for analytic signal construction. HHT has achieved remarkable success across diverse fields including seismology, meteorology, and financial analysis, demonstrating its versatility and analytical power. Consequently, HHT is recognized as a fully reliable analytical methodology with superior performance characteristics and broad application prospects in modern signal processing systems.