A useful input parameterization for optimal experiment design

Optimal inputs are usually, determined by minimizing a scalar-valued function of the inverse Fisher information matrix. The function should be monotonically increasing. This is the case, e.g., for the trace and the determinant. The minimization must be performed under some constraints to prevent the input or output amplitude to blow up. In this note it is proved that, assuming open-loop experiments, the optimal input signal can be realized as a certain ARMA process of low order (or, at least, can be approximated with any degree of accuracy by such a process). This allows the optimal input design problem to be reformulated as a standard static optimization problem of low dimension.