Key note lecture on 27th March 2015 by Eckhard Hitzer (ICU, Tokyo, Japan) on “Overview of Quaternion and Clifford Fourier Transforms” for the Asian Workshop on Clifford’s Geometric Algebra and Information Technology (AWCGAIT2015) at the Danang University of Science and Technology, Vietnam, 26-28 March 2015. The conference was organized by Prof. M. T. Pham, Head of Networks and Communication Department – IT Faculty, and his colleagues. The lecture was digitally recorded by Ass. Prof. K. Tachibana of Kogakuin University in Tokyo, Japan.
The lecture is given in English, followed by a short summary in Vietnamese.
Lecture slides: here.
Abstract: After a brief definition of quaternion algebra and Clifford algebra, we will explain how the complex Fourier transform can be generalized to these non-commutative algebras. We will see that the non-commutativity of signal and transformation kernel under the integral leads to interesting new properties with clear benefits for applications. Such benefits are rotation covariance, multidimensional phase concept, and use of the algebra basis to split a signal into a refined set of components with well defined symmetries, etc.
Source: https://www.youtube.com/watch?v=qm5I_D9NN3g, 31 Mar. 2015