Frequency Response Function Measurements via Local Rational Modeling, Revisited

A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leakage) errors cause important bias and variance errors in the FRF estimate. To decrease these errors, several local modeling techniques have been proposed in the literature. This article presents an overview of the existing methods and gives an in-depth bias and variance analysis of the FRF and disturbing noise variance estimates. In addition, a new local modeling approach is described, which combines the small bias error of the local rational approximation with the low noise sensitivity of the local polynomial approximation. It is based on an automatic local model-order selection procedure applied to a specific subclass of rational functions.