Volterra filter equalization: a fixed point approach

One important application of Volterra filters is the equalization of nonlinear systems. Under certain conditions, this problem can be posed as a fixed point problem involving a contraction mapping. We generalize the previously studied local inverse problem to a very broad class of equalization problems. We also demonstrate that subspace information regarding the response behavior of the Volterra filters can be incorporated to improve the theoretical analysis of equalization algorithms. To this end, a new "windowed" signal norm is introduced. Using this norm, we show that the class of allowable inputs is increased and the upper bounds on the convergence rate are improved when subspace information is exploited.