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Measuring the best linear approximation of a nonlinear system with uniformly frequency-distributed periodic signals

This paper studies the approximation, in least square sense, of a nonlinear system with a linear system, when the measurements are made with periodic signals with a high number of harmonics. The dependency of the asymptotic (period length tends to infinity) behavior of the best linear approximation on the local selection scheme for the excited frequencies is analyzed in detail. Under some weak conditions, error bounds and a full equivalence with random noise excitations is established.