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

DOI10.1007/S00006-014-0441-9zbMath1301.42017arXiv1306.2092OpenAlexW2072343406MaRDI QIDQ742340

Eckhard M. S. Hitzer

Publication date: 18 September 2014

Published in: Advances in Applied Clifford Algebras (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.2092

zbMATH Keywords

Clifford algebrasignal processingClifford Fourier transformsquare roots of \(-1\)

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Clifford algebras, spinors (15A66)

Related Items (16)

General two-sided quaternion Fourier transform, convolution and mustard convolution ⋮ Quaternionic Wiener-Khinchine theorems and spectral representation of convolution with steerable two-sided quaternion Fourier transform ⋮ Generalization of Titchmarsh's theorems for the Minkowski algebra ⋮ Generalized uncertainty principles associated with the quaternionic offset linear canonical transform ⋮ Two-sided fractional Clifford–Fourier transformation ⋮ General steerable two-sided Clifford Fourier transform, convolution and mustard convolution ⋮ Three‐dimensional generalized analytic signal associated with linear canonical transform in Clifford biquaternion domain ⋮ Uncertainty principles of the fractional Clifford–Fourier transform ⋮ Two-sided Clifford wavelet function in \(Cl(p, q)\) ⋮ Boas type results for two-sided quaternion Fourier transform and uniform Lipschitz spaces ⋮ Two-sided Fourier transform in Clifford analysis and its application ⋮ Heisenberg's and Hardy's uncertainty principles for special relativistic space-time Fourier transformation ⋮ Uncertainty principle for space-time algebra-valued functions ⋮ The Wigner-Ville distribution associated with the quaternion offset linear canonical transform ⋮ The continuous quaternion algebra-valued wavelet transform and the associated uncertainty principle ⋮ A new uncertainty principle related to the generalized quaternion Fourier transform

Uses Software

• BIGEBRA
• CLIFFORD
• Maple

Cites Work

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• Applications of Clifford's geometric algebra
• Geometric roots of \(-1\) in Clifford algebras \(C \ell_{p,q}\) with \(p + q \leq 4\)
• Clifford and Graßmann Hopf algebras via the BIGEBRA package for Maple
• Biquaternion (complexified quaternion) roots of \(- 1\)
• The Hermitian Clifford analysis toolbox
• Clifford Fourier transform on multivector fields and uncertainty principles for dimensions \(n=2\pmod 4\) and \(n=3\pmod 4\)
• A general geometric Fourier transform convolution theorem
• Convolution products for hypercomplex Fourier transforms
• Quaternion Fourier transform on quaternion fields and generalizations
• Computations with Clifford and Grassmann algebras
• The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations
• Square Roots of –1 in Real Clifford Algebras
• A General Geometric Fourier Transform
• Clifford–Fourier Transform and Spinor Representation of Images
• Clifford–Fourier Transform for Color Image Processing
• Hypercomplex Fourier Transforms of Color Images
• Clifford algebras, Fourier transforms, and quantum mechanics
• Generalized Exponentials through Appell sets in R[sup n+1 and Bessel functions]
• Directional uncertainty principle for quaternion Fourier transform

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