Abstract
The recently proposed generalized spline nonlinear adaptive filter (GSNAF) can model systems with hard nonlinearity at low computational cost. In this paper, a spline activation function (SAF) is first extended to a two-dimensional function with two sets of inputs to work well in modeling nonlinear systems with cross terms that are products of the time shifted input signals. Then, to prevent the updating of the control points of little significance, the updating algorithm is derived by combining a L1-norm penalty on the control points with the squared error cost function. Some simulations show that the proposed filter can provide comparable or better performance compared to third-order Volterra filters, and GSNAF.
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