A generalization of the octonion Fourier transform to 3-D octonion-valued signals: properties and possible applications to 3-D LTI partial differential systems

DOI10.1007/s11045-020-00706-3zbMath1448.94051arXiv1905.12631OpenAlexW3010579582MaRDI QIDQ2211674

Łukasz Błaszczyk

Publication date: 12 November 2020

Published in: Multidimensional Systems and Signal Processing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.12631

zbMATH Keywords

hypercomplex algebrasoctonion Fourier transformCayley-Dickson numbersmultidimensional linear time-invariant systems

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (6)

Octonion offset linear canonical transform ⋮ Beurling's theorem associated with octonion algebra valued signals ⋮ Octonion short‐time linear canonical transform ⋮ The uncertainty principle for the octonion Fourier transform ⋮ Discrete octonion Fourier transform and the analysis of discrete 3-D data ⋮ Octonion Fourier transform of Lipschitz real-valued functions of three variables on the octonion algebra

Cites Work

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• Compressed sensing for quaternionic signals
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• The unified theory of \(n\)-dimensional complex and hypercomplex analytic signals
• Quaternion Fourier Transforms for Signal and Image Processing
• Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case

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