Finite-data nonparametric frequency response evaluation without leakage

Abstract

The existing nonparametric frequency response estimation methods suffer from leakage. Because of this, these methods do not yield the correct result in case of exact data of a linear time-invariant system. Our main contribution is a time-domain direct data-driven nonparameteric frequency response estimation method that, in case of exact data satisfying standard persistency of excitation condition, eliminates the leakage and has infinite frequency resolution. The method is derived in the behavioral setting. It requires solving a system of linear equations and has no hyper-parameters. In case of noisy data, a modification of the method with preprocessing with low-rank approximation results in a subspace-type method for frequency response estimation.