On 4-Dimensional Hypercomplex Algebras in Adaptive Signal Processing

  • Francesca OrtolaniEmail author
  • Danilo Comminiello
  • Michele Scarpiniti
  • Aurelio Uncini
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 102)


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.


Adaptive filters Quaternions Tessarines Hypercomplex Widely linear Least mean square 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Francesca Ortolani
    • 1
    Email author
  • Danilo Comminiello
    • 1
  • Michele Scarpiniti
    • 1
  • Aurelio Uncini
    • 1
  1. 1.Dpt. of Information Engineering, Electronics and Telecommunications (DIET)“Sapienza” University of RomeRomeItaly

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