An uncertainty principle for quaternion Fourier transform

DOI10.1016/j.camwa.2008.05.032zbMath1165.42310OpenAlexW2161478868MaRDI QIDQ2389726

Akihisa Hayashi, Mawardi Bahri, Ryuichi Ashino, Eckhard M. S. Hitzer

Publication date: 18 July 2009

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2008.05.032

zbMATH Keywords

uncertainty principlequaternion algebraquaternionic Fourier transformhypercomplex functionsGaussian quaternion signal

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15)

Related Items (53)

Paley-Wiener theorems for the two-sided quaternion Fourier transform ⋮ Uncertainty principle for measurable sets and signal recovery in quaternion domains ⋮ Real Paley–Wiener theorem for the quaternion Fourier transform ⋮ Some results on the lattice parameters of quaternionic Gabor frames ⋮ Tighter uncertainty principles based on quaternion Fourier transform ⋮ Uncertainty principles for the two-sided quaternion linear canonical transform ⋮ Boundedness and uniqueness of quaternion Weyl transform ⋮ A modified uncertainty principle for two-sided quaternion Fourier transform ⋮ Novel uncertainty principles for two-sided quaternion linear canonical transform ⋮ Multidimensional quaternionic Gabor transforms ⋮ Continuous quaternion fourier and wavelet transforms ⋮ A variation on uncertainty principle and logarithmic uncertainty principle for continuous quaternion wavelet transforms ⋮ A simplified proof of uncertainty principle for quaternion linear canonical transform ⋮ On uncertainty principle for quaternionic linear canonical transform ⋮ Uncertainty principle for the two sided quaternion windowed Fourier transform ⋮ Uncertainty principles for Wigner-Ville distribution associated with the quaternion offset linear canonical transform ⋮ Donoho-Stark's uncertainty principle for the quaternion Fourier transform ⋮ Titchmarsh's theorem and some remarks concerning the right-sided quaternion Fourier transform ⋮ General right-sided orthogonal 2D-planes split quaternionic wave-packet transform ⋮ Characterization of rationally sampled quaternionic dual Gabor frames ⋮ Uncertainty principles associated with quaternion linear canonical transform and their estimates ⋮ Pseudo‐differential operator in quaternion space ⋮ Phase retrieval in quaternion Euclidean spaces ⋮ Hyperbolic linear canonical transforms of quaternion signals and uncertainty ⋮ General double-sided orthogonal planes split QFT and wavelet transform on functions and distribution spaces ⋮ Quaternionic Gabor frame characterization and the density theorem ⋮ Tighter Heisenberg-Weyl type uncertainty principle associated with quaternion wavelet transform ⋮ Uncertainty principles related to quaternionic windowed Fourier transform ⋮ Two-sided Fourier transform in Clifford analysis and its application ⋮ Miyachi's theorem for the quaternion Fourier transform ⋮ Uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform ⋮ Relaxed quaternionic Gabor expansions at critical density ⋮ Paley-Wiener and Boas theorems for the quaternion Fourier transform ⋮ Pitt's inequality and the uncertainty principle associated with the quaternion Fourier transform ⋮ Some results for the two-sided quaternionic Gabor Fourier transform and quaternionic Gabor frame operator ⋮ Uncertainty principle for the two-sided quaternion windowed Fourier transform ⋮ A sharp Clifford wavelet Heisenberg-type uncertainty principle ⋮ Lifting of quaternionic frames to higher dimensions with partial ridges ⋮ Quaternion Fourier transform and generalized Lipschitz classes ⋮ Clifford algebras, Fourier transforms, and quantum mechanics ⋮ Plancherel theorem and quaternion Fourier transform for square integrable functions ⋮ Compressed sensing for quaternionic signals ⋮ The Balian-Low theorem for the windowed quaternionic Fourier transform ⋮ Uncertainty principles associated with quaternionic linear canonical transforms ⋮ Clifford wavelet transform and the uncertainty principle ⋮ Convolution theorems for quaternion Fourier transform: properties and applications ⋮ Novel uncertainty principles associated with 2D quaternion Fourier transforms ⋮ On uncertainty principle for the two-sided quaternion linear canonical transform ⋮ Extra-strong uncertainty principles in relation to phase derivative for signals in Euclidean spaces ⋮ A variation on uncertainty principles for quaternion linear canonical transform ⋮ The quaternion Fourier and wavelet transforms on spaces of functions and distributions ⋮ Wigner-Ville distribution and ambiguity function associated with the quaternion offset linear canonical transform ⋮ Multilinear Localization Operators Associated to Quaternion Fourier Transforms

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• Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT
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• CLIFFORD ALGEBRA Cl_3,0-VALUED WAVELET TRANSFORMATION, CLIFFORD WAVELET UNCERTAINTY INEQUALITY AND CLIFFORD GABOR WAVELETS

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