An analysis of THz-TDS signals using geometric algebra

Abstract

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.