https://scigraph.springernature.com/explorer/license/
chapters
2019-04-15T11:17
187-207
false
Harmonic transforms, and among those especially the Fourier transform, play an essential role in mathematical analysis, in almost any part of modern physics, as well as in electrical engineering. The analysis of the following four chapters is motivated by the use of the Fourier transform in signal processing. It turns out that some powerful concepts of one-dimensional signal theory can hardly be carried over to the theory of n-dimensional signals by using the complex Fourier transform. We start by introducing and studying the hypercomplex Fourier transforms in the following two chapters. In this chapter representations in non-commutative algebras are investigated, while chapter 9 is concerned with representations in commutative hypercomplex algebras. After these rather theoretical investigations we turn towards practice in chapter 10 where fast algorithms for the transforms are presented and in chapter 11 where local quaternion-valued LSI-filters based on the quaternionic Fourier transform are introduced and applied to image processing tasks.
2001-01-01
chapter
http://link.springer.com/10.1007/978-3-662-04621-0_8
2001
Non-commutative Hypercomplex Fourier Transforms of Multidimensional Signals
en
Gerald
Sommer
Felsberg
Michael
Pure Mathematics
978-3-662-04621-0
Geometric Computing with Clifford Algebras
978-3-642-07442-4
readcube_id
497c66c3ffb14a54f1fb8061a6d0e88aa8bc02020bc5bbd96d1369b4a7f90897
Bülow
Thomas
Springer Nature - SN SciGraph project
10.1007/978-3-662-04621-0_8
doi
Berlin, Heidelberg
Springer Berlin Heidelberg
Sommer
Gerald
Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, Germany
Kiel University
Mathematical Sciences
dimensions_id
pub.1015423218