A General Geometric Fourier Transform

DOI10.1007/978-3-0348-0603-9_8zbMath1273.15020arXiv1306.2184OpenAlexW1621419977MaRDI QIDQ2847059

Roxana Bujack, Gerik Scheuermann, Eckhard M. S. Hitzer

Publication date: 4 September 2013

Published in: Quaternion and Clifford Fourier Transforms and Wavelets (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.2184

zbMATH Keywords

Fourier transformimage processingshiftscalingClifford algebrageometric algebralinearity

Mathematics Subject Classification ID

Functions of hypercomplex variables and generalized variables (30G35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Clifford algebras, spinors (15A66) Quadratic spaces; Clifford algebras (11E88)

Related Items (14)

Some properties of the spinor Fourier transform ⋮ Quaternion and fractional Fourier transform in higher dimension ⋮ General steerable two-sided Clifford Fourier transform, convolution and mustard convolution ⋮ A general geometric Fourier transform convolution theorem ⋮ Complex and hypercomplex discrete Fourier transforms based on matrix exponential form of Euler's formula ⋮ A sharp Clifford wavelet Heisenberg-type uncertainty principle ⋮ Tensor transform-based quaternion Fourier transform algorithm ⋮ Convolution products for hypercomplex Fourier transforms ⋮ Clifford wavelet transform and the uncertainty principle ⋮ Bochner-Minlos theorem in the frame of real Clifford algebras ⋮ Sharp inequalities for geometric Fourier transform and associated ambiguity function ⋮ Demystification of the geometric Fourier transforms and resulting convolution theorems ⋮ Two-sided Clifford Fourier transform with two square roots of \(-1\) in \(Cl(p,q)\) ⋮ New type of Gegenbauer-Hermite monogenic polynomials and associated Clifford wavelets

Cites Work

• Unnamed Item
• Unnamed Item
• Geometric roots of \(-1\) in Clifford algebras \(C \ell_{p,q}\) with \(p + q \leq 4\)
• Clifford algebra to geometric calculus. A unified language for mathematics and physics
• Clifford Fourier transform on multivector fields and uncertainty principles for dimensions \(n=2\pmod 4\) and \(n=3\pmod 4\)
• Hypercomplex Fourier and Laplace transforms. I
• The Clifford-Fourier integral kernel in even dimensional Euclidean space
• The two-dimensional Clifford-Fourier transform
• Quaternion Fourier transform on quaternion fields and generalizations
• The Clifford-Fourier transform
• Square Roots of –1 in Real Clifford Algebras
• The Cylindrical Fourier Transform
• Clifford–Fourier Transform for Color Image Processing
• Trivector Fourier transformation and electromagnetic field
• Hypercomplex Fourier Transforms of Color Images
• Programming Languages: Principles and Paradigms

This page was built for publication: A General Geometric Fourier Transform