Adaptive smoothing methods for frequency-function estimation

Abstract

The determination of resolution parameter when estimating frequency functions of linear systems is a trade-off 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 benefit is that the tuning can be performed locally, i.e., that different resolutions can be used in different 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 a numerical simulation.