Adaptive Smoothing Methods for Frequency-Domain Identification

The determination of resolution parameter when estimating frequency functions of linear systems is a trade-o between bias and variance. Traditional approaches, like \window-closing" employ a global resolution parameter { the window width { that is tuned by ad hoc methods, usually visual inspection of the results. Here we explore more sophisticated estimation methods, based on local polynomial modeling, that tune such parameters by automatic procedures. A further benet is that the tuning can be performed locally, i.e., that dierent resolutions can be used in dierent frequency bands. The approach is thus a conceptually simple and useful alternative to more established multi-resolution techniques like wavelets. The advantages of the method are illustrated in two numerical examples.