Nonparametric estimation of a time-variant system: An experimental study of B-splines and the regularization based smoothing

In this work linear time varying systems are nonparametrically estimated in the time domain. The key idea is that the classical -one dimensional- impulse response function (IRF) can be extended to a two dimensional form to describe the time varying behavior. Unlike linear time invariant systems where the IRF is unique, the time varying impulse response is not restricted to only one possibility for given input and output signals. To decrease this freedom, additional constraints can be imposed. In this particular case, it is imposed that the IRF and the time variations are smooth. In this paper two different smoothing techniques -B-spline and regularization- are applied in two dimensions: once over the system time (impulse response direction) and once over the global time (referring to the system memory).