The identification of polynomial systems by means of higher order spectra

Following a number of earlier authors, we define a polynomial system as a system that carries a signal of the form X₁( t) + αX₂( t), - ∞ < t < ∞, over into a signal that is a polynomial in α. We consider systems that are polynomial and time invariant. Higher order transfer functions are defined and the problem of their estimation by (i) probing with cosinusoids, (ii) probing with Gaussian signals, is considered. The usual procedures, for the identification of time invariant linear systems, are particular cases of our procedures.