16 February 2009 An analysis of THz-TDS signals using geometric algebra
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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 imensionality 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.
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Weixin Xie, Weixin Xie, Jing Li, Jing Li, Jihong Pei, Jihong Pei, } "An analysis of THz-TDS signals using geometric algebra", Proc. SPIE 7277, Photonics and Optoelectronics Meetings (POEM) 2008: Terahertz Science and Technology, 72770E (16 February 2009); doi: 10.1117/12.820984; https://doi.org/10.1117/12.820984

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