Algebraic foundations of split hypercomplex nonlinear adaptive filtering |
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Authors: | E. Hitzer |
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Affiliation: | Department of Applied Physics, University of Fukui, , 910‐8507 Fukui, Japan |
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Abstract: | A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g., for quaternions). Already in the case of quaternions, we can predict improvements in performance of hypercomplex processes. The convergence of the proposed algorithms is rigorously analyzed. Copyright © 2012 John Wiley & Sons, Ltd. |
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Keywords: | quaternionic adaptive filtering hypercomplex adaptive filtering nonlinear adaptive filtering hypercomplex multilayer perceptron Clifford geometric algebra |
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