Special Colloquium: Norden E. Huang

Title: On Holo-Hilbert Spectral Analysis

Speaker: Norden E. Huang

                Innovation Center

  First Institute of Oceanography and

  Center for Nonlinear Sciences,

  Qingdao National Laboratory for Marine Science and Technology

Place: Room 201, Building 12, Yuquan Campus

Time: Oct. 25^th , Thursday, 15:00-16:00

Abstract

Traditionally, spectral analysis is defined as transform the time domain data to frequency domain. It is achieved through integral transforms based on additive expansions of a priori determined basis, under linear and stationary assumptions.  For nonlinear processes, the data can have both amplitude and frequency modulations generated by intra-wave and inter-wave interactions involving both additive and nonlinear multiplicative processes. Under such conditions, the additive expansion could not fully represent the physical processes resulting from multiplicative interactions. Unfortunately, all existing spectral analysis methods are based on additive expansions, based either on a priori or adaptive bases. While the adaptive Hilbert spectral analysis could accommodate the intra-wave nonlinearity, the inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase lock modulations are left untreated. To resolve the multiplicative processes, we propose a full informational spectral representation: The Holo-Hilbert Spectral Analysis (HHSA), which would accommodate all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions, through additional dimensions in the spectrum to account for both the variations in frequency and amplitude modulations (FM and AM) simultaneously. Applications to wave-turbulence interactions to brain electric waves will be presented to demonstrate the usefulness of this new spectral representation.

References

Norden E Huang, Kun Hu, Albert CC Yang, Hsing-Chih Chang, Deng Jia, Wei-Kuang Liang, Jia Rong Yeh, Chu-Lan Kao, Chi-Hung Juan, Chung Kang Peng, Johanna H Meijer, Yung-Hung Wang, Steven R Long, Zhauhua Wu, 2016: On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data.  Phil. Trans. R. Soc. A 374 (2065), 20150206, 2016

About the Speaker

Dr. Norden Huang holds a BS Engineering Degree from National Taiwan University (19690) and a PhD in fluid mechanics and mathematics from the Johns Hopkins University (1967). Currently, he is the founding directors for the Innovation Center and the Data Analysis Laboratory at the First Oceanographic Institute, SOA, Qingdao.  He was also the founding directors of the Research Center for Adaptive Data Analysis and Research Center for Dynamical Biomarkers and Translational Medicine at the National Central University, Zhongli, Taiwan, China (2006-2017).  Most of his career is in NASA (1975-2006), where he had developed the adaptive Hilbert-Huang Transform (HHT), designed to analyze nonstationary and nonlinear data. For this invention, he was awarded the 1998 NASA Special Space Act Award with the citation, ‘[Dr. Huang’s new method] is one of the most important discoveries in the field of applied mathematics in NASA history.’  ‘For contributions to the analysis of nonlinear stochastic signals and related mathematical applications in engineering, biology, and other sciences (NAE Citation),’ he was elected as members of the National Academy of Engineering, 2000; Academia Sinica, 2004; and a Foreign Member of the Chinese Academy of Engineering, 2006.

Recently, he has developed the Holo-Hilbert Spectral Analysis (HHSA) and Intrinsic Probability Density distribution, which reveal new information on inter-wave interactions for nonlinear and nonstationary phenomena. Applications of HHSA on EEG and turbulence data are the areas of his active research, with the collaboration with Oxford University Center for Human Brain Activity and Harvard and Stanford Medical School.