An Analysis of THz-TDS Signals using Geometric Algebra

机译：使用几何代数分析THz-TDS信号

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THz-TDS signals can be represented as vectors in a high dimensional vector space, which are hyper-complex numbers in geometric algebra (GA). Using the language of GA, the properties of these vectors are theoretically analyzed and demonstrate the projective character of THz-TDS signals. The tangential distance of vectors is used to measure the difference of the corresponding THz-TDS signals. A novel dimensionality reduction method via the projective split is presented, by which vectors of THz-TDS signals can be linear mapped from a high dimensional space into a lower dimensional space. The projective split is recursively employed and linear maps the vector space of high dimension into a sequence of sub-spaces step by step. Experiments demonstrate the feasibility and accuracy of our method.

机译：THz-TDS信号可以表示为高维向量空间中的向量，这是几何代数（GA）中的超复数。使用遗传算法的语言，从理论上分析了这些矢量的特性，并证明了THz-TDS信号的投影特性。向量的切线距离用于测量相应的THz-TDS信号的差。提出了一种新的通过射影分裂的降维方法，通过该方法可以将THz-TDS信号的矢量从高维空间线性映射到低维空间。递归地采用投影分割，并将高维向量空间逐步映射为一系列子空间。实验证明了该方法的可行性和准确性。

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来源
《Photonics and optoelectronics meetings;Conference on terahertz science and technology;POEM; 20081124-27;20081124-27;20081124-27; Wuhan(CN);Wuhan(CN);Wuhan(CN)》|2008年|P.72770E.1-72770E.8|共8页
会议地点 Wuhan(CN);Wuhan(CN);Wuhan(CN)
作者
Weixin Xie; Jing Li; Jihong Pei;
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作者单位

School of Electronic Engineering, Xidian University, Xi'an 710071, P. R. China Intelligent Information Institute, Shenzhen University, Shenzhen, 518060, P. R. China;

School of Electronic Engineering, Xidian University, Xi'an 710071, P. R. China Intelligen;

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原文格式 PDF
正文语种 eng
中图分类光电子技术、激光技术;
关键词
THz-TDS; geometric algebra; projective split;

机译：THz-TDS;几何代数;射影分裂;

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An Analysis of THz-TDS Signals using Geometric Algebra

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