Non-commutative Hypercomplex Fourier Transforms of Multidimensional Signals View Full Text


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Chapter Info

DATE

2001

AUTHORS

Thomas Bülow , Michael Felsberg , Gerald Sommer

ABSTRACT

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. More... »

PAGES

187-207

Book

TITLE

Geometric Computing with Clifford Algebras

ISBN

978-3-642-07442-4
978-3-662-04621-0

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-662-04621-0_8

DOI

http://dx.doi.org/10.1007/978-3-662-04621-0_8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1015423218


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