The quaternion domain Fourier transform and its properties

DOI10.1007/s00006-015-0620-3zbMath1350.42018OpenAlexW2178803062MaRDI QIDQ331628

Eckhard M. S. Hitzer

Publication date: 27 October 2016

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

Full work available at URL: https://doi.org/10.1007/s00006-015-0620-3

zbMATH Keywords

uncertaintyFourier transformimage processingquaternionssignalsorthogonal transformationsquaternionic differential operators

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Clifford algebras, spinors (15A66) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Related Items

Donoho-Stark's uncertainty principle for the quaternion Fourier transform ⋮ Characterization of rationally sampled quaternionic dual Gabor frames ⋮ Uncertainty principles associated with quaternion linear canonical transform and their estimates ⋮ General double-sided orthogonal planes split QFT and wavelet transform on functions and distribution spaces ⋮ Quaternionic Gabor frame characterization and the density theorem ⋮ Quaternion Fourier transform and generalized Lipschitz classes ⋮ Quaternionic inverse Fourier transforms on locally compact abelian groups ⋮ Plancherel theorem and quaternion Fourier transform for square integrable functions ⋮ Two-sided fractional quaternion Fourier transform and its application

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Clifford algebra unveils a surprising geometric significance of quaternionic root systems of Coxeter groups
• Multi-resolution image analysis using the quaternion wavelet transform
• Quaternion Fourier transform on quaternion fields and generalizations
• Zur Theorie der regulären Funktionen einer Quaternionen-Variablen
• Quaternion and Clifford Fourier Transforms and Wavelets
• The Orthogonal 2D Planes Split of Quaternions and Steerable Quaternion Fourier Transformations
• Quaternionic Spectral Analysis of Non-Stationary Improper Complex Signals
• Hypercomplex Fourier Transforms of Color Images
• Quaternionic analysis
• A concise quaternion geometry of rotations
• Quaternions and Reflections
• Directional uncertainty principle for quaternion Fourier transform