Three Implementation Methods of Hilbert-Huang Transform (HHT)

There are three primary implementation methods for the Hilbert-Huang Transform (HHT), particularly suitable for beginners interested in mastering this powerful signal processing technique. Each method offers unique advantages for different applications.

The Classical Empirical Mode Decomposition (CEMD) method serves as the fundamental approach, ideal for analyzing nonlinear and non-stationary signals. This algorithm operates by iteratively sifting the original signal to extract Intrinsic Mode Functions (IMFs) representing different oscillatory modes. In code implementation, this typically involves: 1) Identifying all local extrema, 2) Generating upper/lower envelopes via cubic spline interpolation, 3) Calculating mean envelopes, and 4) Iteratively extracting IMFs until stoppage criteria are met. Each IMF can then undergo Hilbert transform to obtain instantaneous frequency, amplitude, and phase information.

The Ensemble Empirical Mode Decomposition (EEMD) method enhances CEMD by addressing mode mixing issues through noise-assisted analysis. The implementation involves: 1) Adding multiple realizations of white noise to the original signal, 2) Performing EMD on each noise-added signal, 3) Ensemble averaging the corresponding IMFs. Key programming considerations include determining optimal noise amplitude (typically 0.2 times standard deviation) and ensemble size (usually 100-500 trials) to balance computational efficiency and decomposition quality.

The Complete Ensemble EMD with Adaptive Noise (CEEMDAN) represents the most advanced approach, particularly effective for noisy signals and incomplete datasets. This algorithm improves upon EEMD by: 1) Adaptively controlling noise amplitude at each decomposition stage, 2) Using unique noise realizations for each IMF extraction, 3) Implementing residue-based stopping criteria. Implementation typically requires careful management of adaptive noise parameters and efficient computation of multiple decomposition rounds.

HHT remains a powerful technique offering significant advantages for modern signal processing applications. Selecting the appropriate implementation method based on signal characteristics and computational requirements enables researchers to extract valuable insights and advance analytical capabilities across various domains.