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Signal, Image and Video Processing

, Volume 6, Issue 3, pp 381–388 | Cite as

Fractional Fourier transforms of hypercomplex signals

  • Hendrik De BieEmail author
  • Nele De Schepper
Original Paper

Abstract

An overview is given to a new approach for obtaining generalized Fourier transforms in the context of hypercomplex analysis (or Clifford analysis). These transforms are applicable to higher-dimensional signals with several components and are different from the classical Fourier transform in that they mix the components of the signal. Subsequently, attention is focused on the special case of the so-called Clifford-Fourier transform where recently a lot of progress has been made. A fractional version of this transform is introduced and a series expansion for its integral kernel is obtained. For the case of dimension 2, also an explicit expression for the kernel is given.

Keywords

Hypercomplex analysis Fractional transform Generalized Fourier transform Clifford-Fourier transform 

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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of Mathematical Analysis, Faculty of Engineering and ArchitectureGhent UniversityGhentBelgium

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