On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

Abstract

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier integral transform and its high performance digital equivalent - the fast Fourier transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the empirical mode decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source numerical data vector into a finite set of intrinsic mode functions (IMF). These functions form a nearly orthogonal, derived from the data basis (adaptive basis). The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT data processing system (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT EMD algorithm. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2D processing using field programmable gate array (FPGA) computational resources, enhanced HHT synthesis, and will broaden the scope of HHT applications for signal processing.