Enhanced Hilbert-Huang Transform Algorithm with Adaptive IMF Screening

Application Background Empirical Mode Decomposition (EMD) is a signal processing technique that decomposes complex signals into a series of monocomponent signals known as Intrinsic Mode Functions (IMFs). Through Hilbert transform implementation (typically using MATLAB's hilbert() function), instantaneous frequency can be calculated for each IMF component. However, the Hilbert-Huang transform faces significant endpoint effects in practical applications. To address this limitation, we propose an adaptive spurious IMF screening algorithm that utilizes the correlation coefficient between the residual and original signal as a dynamic threshold. Key Technology Complex signals can be decomposed into monocomponent signals through Empirical Mode Decomposition. Any valid Intrinsic Mode Function must satisfy two fundamental conditions during the sifting process: 1. Throughout the entire data length, the number of extrema (maxima and minima) and zero-crossings must be equal or differ by at most one. This condition ensures proper oscillation characteristics. 2. At any data point, the mean value of the envelope defined by local maxima (upper envelope) and the envelope defined by local minima (lower envelope) must be zero. This condition is typically enforced through iterative cubic spline interpolation and mean subtraction operations. The algorithm implementation involves iterative sifting with boundary condition handling using mirror extension or signal prediction techniques to mitigate endpoint effects. The correlation-based thresholding mechanism automatically identifies and eliminates spurious IMF components by comparing residue signal characteristics with the original input. These fundamental concepts of EMD and IMF formulation provide the basis for advanced signal processing applications, which we will explore in detail along with analytical solutions to implementation challenges.