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A General Geometric Fourier Transform Convolution Theorem

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Abstract

The large variety of Fourier transforms in geometric algebras inspired the straight forward definition of “A General Geometric Fourier Transform” in Bujack et al., Proc. of ICCA9, covering most versions in the literature. We showed which constraints are additionally necessary to obtain certain features like linearity, a scaling, or a shift theorem. In this paper we extend the former results by a convolution theorem.

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Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, Johannisgasse 26, 04103, Leipzig, Germany

    Roxana Bujack & Gerik Scheuermann

  2. Department of Applied Physics, University of Fukui, 3-9-1 Bunkyo, Fukui, 910-8507, Japan

    Eckhard Hitzer

Authors
  1. Roxana Bujack
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  2. Gerik Scheuermann
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  3. Eckhard Hitzer
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Correspondence to Roxana Bujack.

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Bujack, R., Scheuermann, G. & Hitzer, E. A General Geometric Fourier Transform Convolution Theorem. Adv. Appl. Clifford Algebras 23, 15–38 (2013). https://doi.org/10.1007/s00006-012-0338-4

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  • DOI: https://doi.org/10.1007/s00006-012-0338-4

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