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

@article{Huang2016OnHS,
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},
year={2016},
volume={374}
}
• 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…
67 Citations

## Figures and Tables from this paper

Revealing the Dynamic Nature of Amplitude Modulated Neural Entrainment With Holo-Hilbert Spectral Analysis
• Biology
Frontiers in Neuroscience
• 2021
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
• Biology
IEEE Transactions on Neural Systems and Rehabilitation Engineering
• 2018
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
• Computer Science
2018 International Conference on Computer Engineering, Network and Intelligent Multimedia (CENIM)
• 2018
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
• Computer Science
International Journal of Engineering & Technology
• 2018
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
• Physics
J. Open Source Softw.
• 2021
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
• Biology
Scientific Reports
• 2019
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
• Computer Science
IEEE Sensors Journal
• 2018
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.

## References

SHOWING 1-10 OF 28 REFERENCES
On Hilbert Spectral Representation: a True Time-Frequency Representation for nonlinear and nonstationary Data
• Mathematics
• 2011
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
• 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
• Mathematics
ArXiv
• 2013
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
• Engineering
• 2009
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
• Mathematics
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
• 2003
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
• Physics
• 2009
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
• Physics
IEEE Transactions on Signal Processing
• 2008
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
• Mathematics