Synthesis of linear stochastic signals in identification problems

Stationary stochastic inputs are generated from linear processes of the autoregressive moving average type. Since the spectral density of such a process is nonzero everywhere, this belongs to the class of admissible signals satisfying identifiability requirements. We obtain a characterization of the optimal signals in terms of their spectral densities using the results on asymptotic eigenvalue distribution of Toeplitz matrices. These signals belong to the general class of random inputs that can be generated using standard instrumentation consisting of delay lines and white noise generator.