Utilization of conditioned higher-order spectra for nonlinear system identification

For higher-order Volterra systems with arbitrary stationary inputs, an orthogonalization scheme based upon ordered sets of conditioned orthogonal higher-order input vectors in the frequency domain using Gram-Schmidt method is presented. A new set of nonlinear transfer functions for the conditioned orthogonal Volterra system is obtained from a coordinate transformation of a Volterra system based upon nonorthogonal higher-order input vectors. The orthogonal modes has the same minimum mean square error as the original system but without hybrid coherences, thus allowing physically meaningful interpretation of nonlinearities of systems