On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

  title={On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data},
  author={Norden E. Huang and Kun Hu and Albert C.-C. Yang and Hsin-Chih Chang and Deng Jia and Wei-Kuang Liang and Jia-Rong Yeh and Chu-Lan Kao and Chi-Hung Juan and Chung-Kang Peng and Johanna H. Meijer and Yung-Hung Wang and Steven R. Long and Zhauhua Wu},
  journal={Philosophical transactions. Series A, Mathematical, physical, and engineering sciences},
  • N. Huang, Kun Hu, Zhauhua Wu
  • Published 13 April 2016
  • Mathematics
  • Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through… 
Revealing the Dynamic Nature of Amplitude Modulated Neural Entrainment With Holo-Hilbert Spectral Analysis
Results from both simulation and SSVEPs demonstrated that temporal dynamic and non-linear CFC features can be revealed with HHSA, and shed new light on further applications in analysis of brain electrophysiological data with the aim of understanding the functional roles of neuronal oscillation in various cognitive functions.
Analyses of EEG Oscillatory Activities During Slow and Fast Repetitive Movements Using Holo-Hilbert Spectral Analysis
The use of HHSA for oscillatory activity analysis can be an efficient tool to provide informative interaction among different frequency bands to study the functional coupling between the primary sensorimotor area and other brain regions.
Spectral Analysis of Familiar Human Voice Based On Hilbert-Huang Transform
A powerful data analysis method called the Hilbert-Huang transform (HHT), which can be used to extract audio frequency components from nonlinear and nonstationary human voice signals, which makes it very extremely versatile to be used for analysing familiar human voices.
Ensemble EMD based Time-Frequency Analysis of Continuous Adventitious Signal Processing
A new method for analysis of two classes of lung signals namely wheezes and crackles based on improved Empirical Mode Decomposition called EEMD to analyze and compare continuous and discontinuous adventitious sounds with EMD is presented.
EMD: Empirical Mode Decomposition and Hilbert-Huang Spectral Analyses in Python
The Empirical Mode Decomposition (EMD) package contains Python (>=3.5) functions for analysis of non-linear and non-stationary oscillatory time series. EMD implements a family of sifting algorithms,
Unraveling nonlinear electrophysiologic processes in the human visual system with full dimension spectral analysis
The findings reveal that the electrophysiological response to amplitude-modulated stimuli is more complex than could be revealed by, for example, Fourier analysis, and highlights the dynamics of neural processes in the visual system.
A Method for Respiration Rate Detection in Wrist PPG Signal Using Holo-Hilbert Spectrum
A Holo-Hilbert spectral analysis (HHSA)-based approach to detect subject’s respiration frequency from wrist photoplethysmogram (PPG) signals has manifested its capability to extract respiration-induced multiplicative component in PPG signal.
Holo-Hilbert spectral-based noise removal method for EEG high-frequency bands


On Hilbert Spectral Representation: a True Time-Frequency Representation for nonlinear and nonstationary Data
The conversion factor turns out to be simply the sampling rate for the full resolution cases and the introduction of this conversion can compare HSA and Fourier spectral analysis results quantitatively.
The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
  • N. Huang, Zheng Shen, Henry H. Liu
  • Mathematics
    Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the ‘empirical mode decomposition’ method with which any complicated data set can be
Sparse Time Frequency Representations and Dynamical Systems
It is shown that each IMF can be associated with a solution of a second order ordinary differential equation of the form $\ddot{x}+p(x,t)\dot{x)+q( x,t)=0$ and a localized variational formulation for this problem is proposed and an effective $l^1$-based optimization method is developed.
On Instantaneous Frequency
This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF, and finds that the NHT and direct quadrature gave the best overall performance.
A confidence limit for the empirical mode decomposition and Hilbert spectral analysis
The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections
Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method
The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.
One or Two Frequencies? The Empirical Mode Decomposition Answers
This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in
The uniqueness of the instantaneous frequency Based on Intrinsic Mode Function
Any IMF can be treated in the form of ai(t) cosθi (t) as the unique defined amplitude-phase pair, from which the instantaneous frequency (IF) can also be determined.
On the trend, detrending, and variability of nonlinear and nonstationary time series
A simple and logical definition of trend is given for any nonlinear and nonstationary time series as an intrinsically determined monotonic function within a certain temporal span, or a function in which there can be at most one extremum within that temporal span.
A Noise-Assisted Data Analysis Method for Automatic EOG-Based Sleep Stage Classification Using Ensemble Learning
This paper investigates the possibility of exploiting the multisource nature of the electrooculography (EOG) signals by presenting a method for automatic sleep staging using the complete ensemble empirical mode decomposition with adaptive noise algorithm, and a random forest classifier.