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Quaternion Fourier Transform on Quaternion Fields and Generalizations

- E. Hitzer
- Mathematics, Computer Science
- ArXiv
- 24 May 2007

TLDR

An uncertainty principle for quaternion Fourier transform

- M. Bahri, E. Hitzer, Akihisa Hayashi, R. Ashino
- Computer Science, Mathematics
- Comput. Math. Appl.
- 1 November 2008

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 bound… Expand

Carrier Method for the General Evaluation and Control of Pose, Molecular Conformation, Tracking, and the Like

- E. Hitzer, K. Tachibana, S. Buchholz, I. Yu
- Mathematics
- 27 February 2009

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. Wedging… Expand

Introduction to Clifford's Geometric Algebra

- E. Hitzer
- Computer Science, Mathematics
- 7 June 2013

TLDR

Multivector differential calculus

- E. Hitzer
- Mathematics
- 1 December 2002

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 the… Expand

Vector Differential Calculus

- E. Hitzer
- Mathematics
- 1 March 2002

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 for… Expand

Directional Uncertainty Principle for Quaternion Fourier Transform

- E. Hitzer
- Mathematics, Physics
- 1 May 2010

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 directional… Expand

Windowed Fourier transform of two-dimensional quaternionic signals

- M. Bahri, E. Hitzer, R. Ashino, R. Vaillancourt
- Mathematics, Computer Science
- Appl. Math. Comput.
- 1 June 2010

TLDR

The Quaternion Domain Fourier Transform and its Properties

- E. Hitzer
- Mathematics
- 1 November 2015

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 valued… Expand

A General Geometric Fourier Transform

- R. Bujack, G. Scheuermann, E. Hitzer
- Mathematics
- 10 June 2013

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 transform… Expand

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