Quadratic system identification using higher order spectra of i.i.d. signals

The properties of higher order moment sequences and higher order spectral moments of an i.i.d. (independent, identically distributed) process up to fourth-order are discussed. These properties are utilized to develop algorithms to identify time-invariant nonlinear systems, which can be represented by second-order Volterra series and which are subjected to an i.i.d. input. A relatively simple solution for estimating the linear and quadratic transfer functions, which requires neither the calculation of the higher order spectral moments of the input for various frequencies nor the calculation of the inverse of matrix, is shown to exist, even though the second-order Volterra series is not an orthogonal model for an i.i.d. input (unless the input is a white Gaussian process)