抄録
This paper deals with a problem of determining optimal periodic test input signals for identification of continuous linear systems under the assumptions that the energy of the periodic input signals is bounded above, that the observed outputs are contaminated with additive white Gaussian noises, and that apriori probability distribution of the unknown system characteristics is white Gaussian and is independent of the observation noises.
By deriving Radon-Nykodim derivatives of the relevant probability measures, the amount of the mutual information between the observed outputs and the unknown system characteristics is calculated in terms of the Fourier coefficients of the test input signals. It is shown that the amount is upper bounded by the energy of the input signals and depends solely upon the auto-correlation of each component of input signals. It is also shown that the bound is really the least upper bound, and that there exist no test input signals that achieve the bound.
A particular consideration is given to the M-sequence signals. It is shown that, as the pulse interval of the M-sequence signals decreases, the corresponding amount of the mutual information tends to the possible upper bound under amplitude as well as energy constraint.
