A Study of Approximation Errors in Local Parametric Approaches to Frequency Response Function Estimation

The concept of local parametric modelling has sparked renewed attention in frequency response function (FRF) measurements. Essentially, these approaches assume a particular parametric structure and approximate the FRF and the leakage errors in a small window around the frequency of interest. Following the successful application of the idea in the local polynomial method (LPM), the local rational method (LRM) was developed. The smoothness of the transfer function in lowly damped systems can be insufficient for polynomial approximation to be effective, provoking us to consider rational functions instead. In this contribution we attempt to quantify the approximation errors when using rational approximants. Of course, observations are always corrupted by noise. However, the impact of disturbances, be it random or bounded, is not within the scope of the current discussion.