  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.
  Keywords: Quaternionic adaptive filtering, Hypercomplex adaptive filtering,
Nonlinear adaptive filtering, Hypercomplex Multilayer Perceptron, Clifford
geometric algebra
