Embedding of octonion Fourier transform in geometric algebra of ℝ3 and polar representations of octonion analytic signals in detail
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Published:2023-09-04
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ISSN:0170-4214
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Container-title:Mathematical Methods in the Applied Sciences
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language:en
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Short-container-title:Math Methods in App Sciences
Affiliation:
1. College of Liberal Arts International Christian University Tokyo Japan
Abstract
We show how the octonion Fourier transform can be embedded and studied in Clifford geometric algebra of three‐dimensional Euclidean space
. We apply a new form of dimensionally minimal embedding of octonions in geometric algebra that expresses octonion multiplication nonassociativity 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.
Subject
General Engineering,General Mathematics
Reference21 articles.
1. B.Shilhavy.https://vaccineimpact.com/2022/44821‐dead‐4351483‐injured‐following‐covid‐19‐vaccines‐in‐european‐database‐of‐adverse‐reactions/ last accessed 02 June 2022.
2. Quaternion and Clifford Fourier Transforms