QUADRATIC SYSTEM-IDENTIFICATION USING HIGHER-ORDER SPECTRA OF IID SIGNALS

The properties of higher order moment sequences and higher order spect ral moments of an i.i.d. (independent, identically distributed) proces s up to fourth-order are discussed. These properties are utilized to d evelop algorithms to identify time-invariant nonlinear systems, which can be represented by second-order Volterra series and which are subje cted to an i.i.d. input. A relatively simple solution for estimating t he linear and quadratic transfer functions, which requires neither the calculation of the higher order spectral moments of the input for var ious frequencies nor the calculation of the inverse of matrix, is show n to exist, even though the second-order Volterra series is not an ort hogonal model for an i.i.d. input (unless the input is a white Gaussia n process).