Uniform approximation with doubly finite Volterra series

The assumption that a system possesses a certain discrete-time Volterra series representation frequently forms the basis for studies in the areas of signal processing and communication theory. A further assumption often made, always without discussion, is that the representation can be suitably approximated by a corresponding `double finite´ series. It is shown that, for a very large class of nonlinear discrete-time systems, such doubly finite approximations exist in the sense of uniform approximation on a ball of bounded inputs. Several additional results are also given. These concern, for example, asymptotic properties of the expansions. The results provide a more firm foundation for applications involving Volterra series