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Hilbert transforms in Clifford analysis

Fred Brackx UGent, Bram De Knock UGent and Hennie De Schepper UGent (2010) Geometric algebra computing : in engineering and computer science. p.163-187
abstract
The Hilbert transform on the real line has applications in many fields. In particular in one–dimensional signal processing, the Hilbert operator is used to extract global as well as instantaneous characteristics, such as frequency, amplitude and phase, from real signals. The multidimensional approach to the Hilbert transform usually is a tensorial one, considering the so-called Riesz transforms in each of the cartesian variables separately. In this paper we give an overview of generalized Hilbert transforms in Euclidean space, developed within the framework of Clifford analysis. Roughly speaking, this is a function theory of higher dimensional holomorphic functions, which is particularly suited for a treatment of multidimensional phenomena since all dimensions are encompassed at once as an intrinsic feature.
Please use this url to cite or link to this publication:
author
organization
year
type
bookChapter
publication status
published
subject
keyword
Clifford analysis, Hilbert transform
book title
Geometric algebra computing : in engineering and computer science
editor
Eduardo Bayro-Corrochano and Gerik Scheuermann
pages
163 - 187
publisher
Springer
place of publication
London, UK
ISBN
9781849961073
9781849961080
DOI
10.1007/978-1-84996-108-0_9
language
English
UGent publication?
yes
classification
B2
copyright statement
I have transferred the copyright for this publication to the publisher
id
1014170
handle
http://hdl.handle.net/1854/LU-1014170
date created
2010-07-26 14:41:40
date last changed
2017-01-02 09:54:28
@incollection{1014170,
  abstract     = {The Hilbert transform on the real line has applications in many fields. In particular in one--dimensional signal processing, the Hilbert operator is used to extract global as well as instantaneous characteristics, such as frequency, amplitude and phase, from real signals. The multidimensional approach to the Hilbert transform usually is a tensorial one, considering the so-called Riesz transforms in each of the cartesian variables separately. In this paper we give an overview of generalized Hilbert transforms in Euclidean space, developed within the framework of Clifford analysis. Roughly speaking, this is a function theory of higher dimensional holomorphic functions, which is particularly suited for a treatment of multidimensional phenomena since all dimensions are encompassed at once as an intrinsic feature.},
  author       = {Brackx, Fred and De Knock, Bram and De Schepper, Hennie},
  booktitle    = {Geometric algebra computing : in engineering and computer science},
  editor       = {Bayro-Corrochano, Eduardo and Scheuermann, Gerik},
  isbn         = {9781849961073},
  keyword      = {Clifford analysis,Hilbert transform},
  language     = {eng},
  pages        = {163--187},
  publisher    = {Springer},
  title        = {Hilbert transforms in Clifford analysis},
  url          = {http://dx.doi.org/10.1007/978-1-84996-108-0\_9},
  year         = {2010},
}

Chicago
Brackx, Fred, Bram De Knock, and Hennie De Schepper. 2010. “Hilbert Transforms in Clifford Analysis.” In Geometric Algebra Computing : in Engineering and Computer Science, ed. Eduardo Bayro-Corrochano and Gerik Scheuermann, 163–187. London, UK: Springer.
APA
Brackx, Fred, De Knock, B., & De Schepper, H. (2010). Hilbert transforms in Clifford analysis. In E. Bayro-Corrochano & G. Scheuermann (Eds.), Geometric algebra computing : in engineering and computer science (pp. 163–187). London, UK: Springer.
Vancouver
1.
Brackx F, De Knock B, De Schepper H. Hilbert transforms in Clifford analysis. In: Bayro-Corrochano E, Scheuermann G, editors. Geometric algebra computing : in engineering and computer science. London, UK: Springer; 2010. p. 163–87.
MLA
Brackx, Fred, Bram De Knock, and Hennie De Schepper. “Hilbert Transforms in Clifford Analysis.” Geometric Algebra Computing : in Engineering and Computer Science. Ed. Eduardo Bayro-Corrochano & Gerik Scheuermann. London, UK: Springer, 2010. 163–187. Print.