Hammerstein uniform cubic spline adaptive filters: Learning and convergence properties

Michele Scarpiniti, Danilo Comminiello, Raffaele Parisi, Aurelio Uncini
2014 Signal Processing  
Keywords: Spline adaptive filter Nonlinear adaptive filter Least mean square Hammerstein system identification Excess mean square error a b s t r a c t In this paper a novel class of nonlinear Hammerstein adaptive filters, consisting of a flexible memory-less function followed by a linear combiner, is presented. The nonlinear function involved in the adaptation process is based on a uniform cubic spline function that can be properly modified during learning. The spline control points are
more » ... ely changed by using gradient-based techniques. This new kind of adaptive function is then applied to the input of a linear adaptive filter and it is used for the identification of Hammerstein-type nonlinear systems. In addition, we derive a simple form of the adaptation algorithm, an upper bound on the choice of the step-size and a lower bound on the excess mean square error in a theoretical manner. Some experimental results are also presented to demonstrate the effectiveness of the proposed method in the identification of high-order nonlinear systems.
doi:10.1016/j.sigpro.2014.01.019 fatcat:564qxtzlq5hafcqkaxmsle43vm