Update on EMD and Hilbert-Spectra Analysis of Time Series

U.S. Patent 6,381,559 presents further information about the method described in "Analyzing Time Series Using EMD and Hilbert Spectra" (GSC-13817), NASA Tech Briefs, Vol. 24, No. 10 (October 2000), page 63. To recapitulate: The method is especially well suited for analyzing time-series data that represent nonstationary and nonlinear physical phenomena. The method is based principally on the concept of empirical mode decomposition (EMD), according to which any complicated signal (as represented by digital samples) can be decomposed into a finite number of functions, called "intrinsic mode functions" (IMFs), that admit well-behaved Hilbert transforms. The local energies and the instantaneous frequencies derived from the IMFs through Hilbert transforms can be used to construct an energy-frequency-time distribution, denoted a Hilbert spectrum. The patent expands on the description in the cited prior article by explaining underlying mathematical principles and describing details of implementation. The patent also describes, as major elements of the method, the options of (1) filtering the original signal by combining a subset of IMFs and (2) fitting a curve to the filtered signal — something that it may not be possible to do with the original signal.