Uniform approximation of discrete shift-varying systems

It is shown that the elements G of a large class of input-output maps can be uniformly and arbitrarily approximated using a certain structure if and only if G is continuous. For the case considered the system inputs and outputs are defined on a discrete set (0, 1, ..., a ₁)x...x(0, 1, ..., a_m), in which a₁, ..., a_m are positive integers. Our approximating structure involves certain functions that can be chosen in different ways. For the special case in which these functions are taken to be certain polynomial functions, the input-output map of our structure is a generalized discrete Volterra series. Our results provide an analytical basis for the use of such series