Hilbert-Huang Transform and Its Applications

Abstract

PREFACEEmpirical mode decomposition (EMD) and Hilbert spectral analysis (HSA) represent a desperate attempt to break the suffocating hold on data analysis by the twin assumptions of linearity and stationarity. To analyze the data from nonlinear and non-stationary processes, various attempts such as Spectrograms, Wavelet analysis, and the Wigner-Ville distribution have been made, but the EMD-HSA approach is unique and different from the existing methods of data analysis. The EMD-HAS is truly an adaptive time-frequency analysis. It does not require an a priori functional basis. Instead, the basis functions are derived adaptively from the data by the EMD sifting procedures; the instantaneous frequencies are computed from derivatives of the phase functions of the Hilbert transform of the basis functions; the final result is presented in the time-frequency space. The EMD-HSA is a magnifying glass for analyzing the data from nonlinear and non-stationary processes. The EMD-HSA results are intriguing and are no longer shackled by spurious harmonics (the artifacts of imposing a linearity property on a nonlinear system) or limited by the uncertainty principle (the consequence of Fourier transform pairs in data analysis).EMD-HSA was originally designed in 1995 specifically to study water surface wave evolution, the phenomenon of high frequency waves with short fetch evolving into low frequency waves at long fetch. With the EMD-HSA method, it was found that the evolution of the waves was not continuous but abrupt, discrete and local. Subsequently, NEH spent two years visiting Caltech at the invitation of Professor Theodore Y. Wu. Under the guidance of Professor Wu and Professor Owen M. Phillips of the Johns Hopkins University, the EMD-HSA method was further developed and various applications explored. Professor Wu designated the method as the Hilbert-Huang Transform (HHT), a name later adopted by NASA to avoid the awkward name of EMD-HSA. It is only fair to say that the HHT would not have been developed without the encouragement and guidance of Professors Wu and Phillips.The HHT's power and effectiveness in data analysis have been demonstrated by its successful application to many important problems covering engineering, biomedical, financial and geophysical data. The mathematical development of the HHT, however, is undergoing the same path as other significant and historical data analysis methods as in Fourier analysis and wavelet analysis: Applications are leading to development, and the mathematical theories are following, since the methods were motivated by applications. Mathematicians' apparent interest in the HHT motivated our organization of an HHT mini-symposium at the joint meeting between This book contains most of the presentations made at the mini-symposium with some additions. The book contents are divided into two groups: the theoretical aspects and the applications, with the applications further grouped into geophysics, structural safety, and visualization. In the theoretical aspects, the chapters cover the a...

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“…The precise estimation of timelags requires an accurate measure of the time- mixing, is a possible outcome if the signal spans a large dynamic frequency range [31].…”

“…The Goddard LSC group applied an unmodelled pipeline based on the HilbertHuang Transform (HHT) [31,32] to the analysis of NINJA data. Because our pipeline …”

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“…..... (4) Where * represents convolution; ŷ(t) = The Hilbert Transform of y(t); h(t) = The time impulse response of Hilbert transformer [ h(t)=1/(пt) ]; y(t) = A real continuous time domain input.…”

“…The development of the Hilbert-Huang Transform (HHT) was inspired by the need to describe non-linear, complex and distorted type of waveforms [4]. Following points can prove that HHT is ideal tool for Heart Sound (PCG) analysis:…”

Foreign Object Detection Based on Circular Bistatic Synthetic Aperture Radar

“…A certain length of the signal is recorded based on the pulse duration and sampling frequency. A Hilbert-Huang transform (HHT) [20,21] is applied on the pulse, to filter the DC value. Fast Fourier Transform (FFT) is then applied on the resultant pulse in order to convert it to the frequency domain.…”