The Two-Sided Gabor Quaternionic Fourier Transform and Uncertainty Principles

DOI10.1007/978-3-030-35202-8_1zbMath1482.42011arXiv1901.01098OpenAlexW3008536661MaRDI QIDQ4992726

M. El Kassimi, Saïd Fahlaoui

Publication date: 10 June 2021

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.01098

zbMATH Keywords

Gabor transformquaternion algebraHeisenberg uncertaintyquaternionic transformlogarithmic uncertainty

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) General harmonic expansions, frames (42C15)

Related Items (3)

Characterization of rationally sampled quaternionic dual Gabor frames ⋮ Quaternionic Gabor frame characterization and the density theorem ⋮ A class of quaternionic Fourier orthonormal bases

Cites Work

• Unnamed Item
• Asymptotic behaviour of the quaternion linear canonical transform and the Bochner-Minlos theorem
• Pitt's inequality and the uncertainty principle associated with the quaternion Fourier transform
• The Balian-Low theorem for the windowed quaternionic Fourier transform
• Windowed Fourier transform of two-dimensional quaternionic signals
• The uncertainty principle for the two-sided quaternion Fourier transform
• Local quaternion Fourier transform and color image texture analysis
• Hypercomplex Fourier Transforms of Color Images
• Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT

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