\(L^\infty\) system approximation algorithms generated by \(\varphi\) summations (Q1129710)

The authors discuss linear \(L^\infty\)-approximation of systems from noisy frequency-domain data. The models are based on discrete partial sum operators generated by \(\varphi\)-summations (like Fejér and La Vallée-Poussin as special cases). The main result of the paper consists in the derivation of upper bounds for such operators and for the approximation error as a function of a specific norm of the Fourier transform of the window \(\varphi\). It has also been shown that the rate of convergence of the approximation error depends on the moments of the Fourier transform of \(\varphi\). The result can be used to design the first step of a two-step approximate \({\mathcal H}^\infty\) identification method with desired approximation and convergence properties.