On Adaptive Smoothing of Empirical Transfer Function Estimates

The determination of the right resolution parameter when estimating frequency functions for 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 suggest an adaptive method that tunes such parameters by an automatic procedure. A further benefit is that the tuning can be done locally, i.e., different resolutions can be used in different frequency bands. The ideas are based on local polynomial regression and the “just-in-time”-model concept. The advantages of the method are illustrated in numerical examples.