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On 4-Dimensional Hypercomplex Algebras in Adaptive Signal Processing

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Neural Advances in Processing Nonlinear Dynamic Signals (WIRN 2017 2017)

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 102))

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Abstract

The degree of diffusion of hypercomplex algebras in adaptive and non-adaptive filtering research topics is growing faster and faster. The debate today concerns the usefulness and the benefits of representing multidimensional systems by means of these complicated mathematical structures and the criterions of choice between one algebra or another. This paper proposes a simple comparison between two isodimensional algebras (quaternions and tessarines) and shows by simulations how different choices may determine the system performance. Some general information about both algebras is also supplied.

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Authors and Affiliations

  1. Dpt. of Information Engineering, Electronics and Telecommunications (DIET), “Sapienza” University of Rome, Via Eudossiana 18, 00184, Rome, Italy

    Francesca Ortolani, Danilo Comminiello, Michele Scarpiniti & Aurelio Uncini

Authors
  1. Francesca Ortolani
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  2. Danilo Comminiello
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  3. Michele Scarpiniti
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  4. Aurelio Uncini
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Corresponding author

Correspondence to Francesca Ortolani .

Editor information

Editors and Affiliations

  1. Dipartimento di Psicologia, Università della Campana Luigi Vanvitelli, Caserta, Italy

    Anna Esposito

  2. Fundació Tecnocampus, Pompeu Fabra University, Mataro, Barcelona, Spain

    Marcos Faundez-Zanuy

  3. Department of Civil, Environmental, Energy, and Material Engineering, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy

    Francesco Carlo Morabito

  4. Laboratorio di Neuronica, Dipartimento Elettronica e Telecomunicazioni, Politecnico di Torino, Torino, Italy

    Eros Pasero

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Ortolani, F., Comminiello, D., Scarpiniti, M., Uncini, A. (2019). On 4-Dimensional Hypercomplex Algebras in Adaptive Signal Processing. In: Esposito, A., Faundez-Zanuy, M., Morabito, F., Pasero, E. (eds) Neural Advances in Processing Nonlinear Dynamic Signals. WIRN 2017 2017. Smart Innovation, Systems and Technologies, vol 102. Springer, Cham. https://doi.org/10.1007/978-3-319-95098-3_12

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