Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q)

Eckhard Hitzer

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arXiv · 1306.2092

Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q)

Eckhard Hitzer

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Abstract

We generalize quaternion and Clifford Fourier transforms to general two-sided Clifford Fourier transforms (CFT), and study their properties (from linearity to convolution). Two general \textit{multivector square roots} $\in \cl{p,q}$ \textit{of} -1 are used to split multivector signals, and to construct the left and right CFT kernel factors. Keywords: Clifford Fourier transform, Clifford algebra, signal processing, square roots of -1 .

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Eckhard Hitzer. 2013-06-10. Two-sided Clifford Fourier transform with two square roots of -1 in Cl(p,q). https://arxiv.org/abs/1306.2092

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