Nonparametric frequency response function estimators based on nonlinear averaging techniques

Nonparametric frequency response function (FRF) estimators based on nonlinear averaging techniques are proposed. Under mild assumptions (which are well satisfied after a discrete Fourier transform) it is shown that their bias is proportional to the fourth-order moments of the perturbing errors on the input-output Fourier coefficients, while, for instance, the bias of the classical H₁ estimator is a function of the second-order moments. Analytical expressions are given for the bias when the frequency-domain input-output errors are zero-mean complex Gaussian (and mutually correlated)