• Publications
  • Influence
Quaternion Fourier Transform on Quaternion Fields and Generalizations
  • E. Hitzer
  • Mathematics, Computer Science
  • ArXiv
  • 24 May 2007
TLDR
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Expand
An uncertainty principle for quaternion Fourier transform
We review the quaternionic Fourier transform (QFT). Using the properties of the QFT we establish an uncertainty principle for the right-sided QFT. This uncertainty principle prescribes a lower boundExpand
Carrier Method for the General Evaluation and Control of Pose, Molecular Conformation, Tracking, and the Like
Abstract.The four basic geometric objects of points, point pairs, circles and spheres correspond to outer product null-spaces constructed by conformal points in conformal geometric algebra. WedgingExpand
Introduction to Clifford's Geometric Algebra
  • E. Hitzer
  • Computer Science, Mathematics
  • 7 June 2013
TLDR
This tutorial explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, and the popular conformal model. Expand
Multivector differential calculus
Universal geometric calculus simplifies and unifies the structure and notation of mathematics for all of science and engineering, and for technological applications. This paper treats theExpand
Vector Differential Calculus
This paper treats the fundamentals of the vector differential calculus part of universal geometric calculus. Geometric calculus simplifies and unifies the structure and notation of mathematics forExpand
Directional Uncertainty Principle for Quaternion Fourier Transform
Abstract.This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directionalExpand
Windowed Fourier transform of two-dimensional quaternionic signals
TLDR
In this paper, we generalize the classical windowed Fourier transform (WFT) to quaternion-valued signals and derive several important properties such as reconstruction formula, reproducing kernel, isometry, and orthogonality relation. Expand
The Quaternion Domain Fourier Transform and its Properties
So far quaternion Fourier transforms have been mainly defined over $${\mathbb{R}^2}$$R2 as signal domain space. But it seems natural to define a quaternion Fourier transform for quaternion valuedExpand
A General Geometric Fourier Transform
The increasing demand for Fourier transforms on geometric algebras has resulted in a large variety. Here we introduce one single straightforward definition of a general geometric Fourier transformExpand
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