Functions and Analysis

    

Embedding of Octonion Fourier Transform in Geometric Algebra of R^3 and Polar Representations of Octonion Analytic Signals in Detail

Authors: Eckhard Hitzer

We show how the octonion Fourier transform can be embedded and studied in Clifford geometric algebra of three-dimensional Euclidean space Cl(3,0). We apply a new form of dimensionally minimal embedding of octonions in geometric algebra, that expresses octonion multiplication non-associativity with a sum of up to four (individually associative) geometric algebra product terms. This approach leads to new polar representations of octonion analytic signals and signal reconstruction formulas.

Comments: 17 Pages. 3 tables, 1 figure. Published in Mathematical Methods in the Applied Sciences, 2023. DOI: 10.1002/mma.9639.

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Submission history

[v1] 2023-08-18 05:57:57

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