Asymptotic properties of transfer function estimates using non-parametric noise models under relaxed assumptions

It is well known that under very general assumptions the discrete Fourier coefficients of filtered noise is asymptotically independent circular complex Gaussian distributed, based on a generalized central limit theorem (CLT). The standard results on the consistency and the asymptotic uncertainty of the frequency domain Errors-in-Variables (EIV) estimator are derived under the assumption that the Fourier coefficients are circular complex Gaussian distributed and independent over the different frequency bins. In this paper, we shall study the influence of this assumption on the consistency and the efficiency of the frequency domain EIV-estimator. We show that a slightly stronger form of the CLT is needed to preserve the classically obtained uncertainty bounds if independent complex Gaussian Fourier coefficients are not assumed. Our analysis reveals that the classical derived asymptotic uncertainty bounds are valid for a very wide class of distributions.