Orthogonal development of a discrete frequency-domain third-order Volterra model

The objective is to present an orthogonal development of a discrete frequency-domain third-order Volterra model valid for general (i.e., non-Gaussian and Gaussian) stationary random inputs. A modified Gram-Schmidt orthogonalization procedure is utilized, and the concept of the generalized system coherency function is extended to the orthogonal model to quantify the goodness of both the model and its constituent linear, quadratic, and cubic components. The practicality and feasibility of the approach are demonstrated by utilizing it to model actual physical nonlinear systems given experimental input-output data from such systems.<>