Volterra representation and Wiener-like identification of nonlinear systems: scope and limitations

Abstract

After the work of Marmarelis & Naka (1972, 1973) in the catfish retina, systems analysis using stochastic stimuli has had a boom in the seventies (e.g. McCann & Marmarelis, 1975; Eckert & Bishop, 1975; French & Wong, 1977; Lipson, 1975; McCann, 1974; Naka, Marmarelis & Chan, 1975; Spekreijse & Reits, 1982; Trimble & Phillips, 1978; Terzuolo et al. 1982). White-noise analysis was considered to be a general tool for investigating nonlinear systems gaining a maximum of information with a minimum of assumptions about the system. The modification of the original Wiener theory (Wiener, 1958; Cameron & Martin, 1947; McKean, 1972) by Lee & Schetzen (1965) made the theory fairly easy to implement into widely available computers and thus accessible to a larger number of experimenters.