A fast adaptive Volterra filter

In this paper, we introduce a general parameterization method of the adaptive Volterra filter, and investigate the convergence of the adaptive parameters. The key of the present method is that the Volterra kernels, which are multi-dimensional functions, are expanded by an arbitrary one-dimensional orthonormal function set. Based on this investigation, we propose an efficient adaptive Volterra filter to reduce the number of the parameters and to make the convergence of the parameters more stable and faster. Finally, we illustrate the usefulness of our filter by numerical simulations.