On adaptive smoothing of empirical transfer function estimates

The determination of the right resolution parameter when estimating frequency functions of linear systems is a trade-off between bias and variance. Traditional non-parametric 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. This paper suggests a method that tunes such parameters by an automatic procedure. A further benefit is that the tuning can be performed locally, i.e., that different resolutions can be used in different frequency bands. The ideas are based on local polynomial regression and a data-driven bandwidth selector. The advantages of the proposed method are illustrated in numerical examples.