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Updated: Mar 24, 2026

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Split quaternion nonlinear adaptive filtering.

Bukhari Che Ujang1, Clive Cheong Took, Danilo P Mandic

  • 1Communications and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. che.che-ujang07@imperial.ac.uk

Neural Networks : the Official Journal of the International Neural Network Society
|November 21, 2009
PubMed
Summary
This summary is machine-generated.

A novel split quaternion learning algorithm enhances adaptive filter training for 4D signals by accounting for quaternion non-commutativity. This approach improves hypercomplex signal processing performance and convergence.

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Area of Science:

  • Signal Processing
  • Adaptive Filters
  • Hypercomplex Analysis

Background:

  • Existing learning algorithms for adaptive filters often neglect the non-commutative nature of quaternion products.
  • Processing of three- and four-dimensional signals requires advanced adaptive filtering techniques.

Purpose of the Study:

  • To propose a split quaternion learning algorithm for training nonlinear finite impulse response adaptive filters.
  • To address the non-commutativity of quaternion products in algorithm derivation.
  • To improve performance in hypercomplex signal processing.

Main Methods:

  • Derivation of a split quaternion learning algorithm considering quaternion non-commutativity.
  • Rigorous mathematical analysis of algorithm convergence.
  • Simulations using benchmark and real-world signals.

Main Results:

  • The proposed algorithm demonstrates improved performance on hypercomplex processes compared to existing methods.
  • Rigorous convergence analysis confirms the stability and effectiveness of the new algorithm.
  • Simulations validate the approach on diverse datasets.

Conclusions:

  • The split quaternion learning algorithm offers a more rigorous and effective method for training adaptive filters for multidimensional signals.
  • Accounting for quaternion algebra's non-commutativity is crucial for enhanced hypercomplex signal processing.
  • The validated algorithm shows promise for real-world applications.