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THz-TDS signal analysis and substance identification via the conformal split

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Abstract

A terahertz time-domain spectroscopy (THz-TDS) imaging system can obtain high-dimensional signals with substance fingerprint information. By introducing geometric algebra, a novel signal analysis approach to THz-TDS signals is developed based on an optical physical mechanism. Using this approach, signals are represented with vectors in the high-dimensional real vector space. Geometric distribution properties and algebraic relationships of THz-TDS signals are deduced. It is proved that every complex refractive index of substances relates to a unique 2-blade, the vectors corresponding to the samples of the same substance are collinear and belong to the intrinsic 2-blade of the substance. When decomposed through the conformal split with respect to a 2-blade, THz-TDS signals of high dimensionality can be related to vectors in a 2-dimensional subspace. Based on the conformal split properties we deduced, two criteria for substance identification on the basis of THz-TDS signals are proposed. Accordingly, a novel substance identification method via the conformal split is presented. In the method, the 2-blade related to each “known” substance is calculated with two vectors corresponding to THz-TDS signals measured from samples of the substance but with different thicknesses. Using the conformal split with respect to those 2-blades, an identified vector corresponding to a THz-TDS signal is linearly related to the vector in a 2-dimensional subspace. The substance of a sample can be identified using criteria on the projected vectors in the subspaces. This method can contribute to accurate classification and identification. Finally, two experiments are presented that show the feasibility and accuracy of this method.

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Authors and Affiliations

  1. School of Electronic Engineering, Xidian University, Xi’an, 710071, China

    WeiXin Xie & Jing Li

  2. Intelligent Information Institute, Shenzhen University, Shenzhen, 518060, China

    WeiXin Xie, Jing Li & JiHong Pei

Authors
  1. WeiXin Xie
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  2. Jing Li
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  3. JiHong Pei
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Correspondence to Jing Li.

Additional information

XIE WeiXin was born in 1941. He received the B.S. degree in signal and information processing from Xidian University, in 1965. He was a visiting scholar at University of Pennsylvania, U.S.A from 1981 to 1983, and from 1989 to 1990. He was a professor of Xidian University since 1986. He was the vice-president of Xidian University from 1992 to 1996. He was the president of Shenzhen University from 1996 to 2005.

Currently, Prof. Xie is the chairman of the Academic Committee of Shenzhen University, and the chairman of the Signal Processing branch of the Chinese Institute of Electronics. He is the EB member of Scichina the primary editor of the Chinese Journal of Signal Processing, and the vice editor of Chinese Journal of Electronics.

PEI JiHong was born in 1966. He received the B.S. degree in electronics engineering from Beihang University in 1989, and the M.Sc. degree in physical electronics and optoelectronics from Xidian University in 1994, and the Ph.D. degree in signal and information processing from Xidian University in 1998. Currently, he is a professor of Shenzhen University. His research interests include intelligent information processing, pattern recognition, video image analysis, THz-TDS signal and image analysis, etc. Prof. Pei is a member of IEEE, a member of the Technical Committee of Multiple-Valued and Fuzzy Logic in China Computer Federation, as well as Technical Committee of Information Fusion in Chinese Society of Aeronautics and Astronautics.

LI Jing was born in 1976. She received the B.S. degree in computer application from Central South University, in 1998, and M.Ss. degree in signal and information processing from Shenzhen University in 2006. She is now a Ph.D. candidate in signal and information processing of school of electronics engineering of Xidian University. Her research interests are signal analysis and process, THz-TDS signal and image analysis, etc.

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Xie, W., Li, J. & Pei, J. THz-TDS signal analysis and substance identification via the conformal split. Sci. China Inf. Sci. 55, 49–63 (2012). https://doi.org/10.1007/s11432-011-4484-4

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  • DOI: https://doi.org/10.1007/s11432-011-4484-4

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