On I1 Approximation and Identification of Discrete-Time Systems

A discrete Fourier transform (DFT) method for l¹ identification of the impulse response of BIBO stable linear systems is studied. First, rate of approximation results are given for l¹ approximation of BIBO stable systems by approximative DFT-based partial sums of Fourier series to understand how the DFT method affects approximative modelling of a BIBO stable impulse response. An l¹ consistency result (in probability) is given for the studied impulse response estimate for strictly stable systems in a stationary noise set-up.