This paper proposes the use of a class of feedforward artificial neura
l networks with polynomial activation functions (distinct for each hid
den unit) for practical modeling of high-order Volterra systems, Discr
ete-time Volterra models (DVM's) are often used in the study of nonlin
ear physical and physiological systems using stimulus-response data, H
owever, their practical use has been hindered by computational limitat
ions that confine them to low-order nonlinearities (i.e., only estimat
ion of low-order kernels is practically feasible), Since three-layer p
erceptrons (TLP's) can be used to represent input-output nonlinear map
pings of arbitrary order, this paper explores the basic relations betw
een DVM and TLP with tapped-delay inputs in the context of nonlinear s
ystem modeling, A variant of TLP with polynomial activation functions-
termed ''separable Volterra networks'' (SVN's)-is found particularly u
seful in deriving explicit relations with DVM and in obtaining practic
able models of highly nonlinear systems from stimulus-response data, T
he conditions under which the two approaches yield equivalent represen
tations of the input-output relation are explored, and the feasibility
of DVM estimation via equivalent SVN training using backpropagation i
s demonstrated by computer-simulated examples and compared with result
s from the Laguerre expansion technique (LET), The use of SVN models a
llows practicable modeling of high-order nonlinear systems, thus remov
ing the main practical limitation of the DVM approach.