Abstract
In this chapter we consider the computational aspect of the quaternionic Fourier transform (QFT), of the Clifford Fourier transform (CFT), and of the commutative hypercomplex Fourier transform (HFT). We can cover all these transforms with the term hypercomplex Fourier transforms, since all mentioned algebras are hypercomplex algebras (see Cha. 9). In order to have a numerical way to evaluate these transforms, we introduce the corresponding discrete transforms by sampling the continuous transforms. Furthermore, we prove the inverse transforms.
This work has been supported by German National Merit Foundation and by DFG Grants So-320-2-1, So-320-2-2, and Graduiertenkolleg No. 357.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Felsberg, M., Bülow, T., Sommer, G., Chernov, V.M. (2001). Fast Algorithms of Hypercomplex Fourier Transforms. In: Sommer, G. (eds) Geometric Computing with Clifford Algebras. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04621-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-662-04621-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07442-4
Online ISBN: 978-3-662-04621-0
eBook Packages: Springer Book Archive