A digital method of modeling quadratically nonlinear systems with a general random input

Without assuming particular statistics of the input, a practical digital method of estimating linear and quadratic transfer functions of a nonlinear time-invariant system that can be described by Volterra series of up to second order is presented. The method is tested and validated by analyzing input-output data of a known quadratically nonlinear system. It is used when there is little knowledge about the input statistics or the input is non-Gaussian. It is also noted that the ordinary coherence functions cannot be used in explaining the input-output power transfer relationship of a quadratic system excited by a non-Gaussian input signal. With respect to the practical application of the method, the relationship between the mean square errors involved in the transfer function estimates and the number of averages taken from the spectral estimation is qualitatively discussed.>