The relation between the sampling time and stochastic error for the impulsive response of linear time-independent systems

In this paper the relation between the variance of the impulsive response samples and the sampling time is analyzed with respect to the identification of a linear time-invariant system with one input and one output. The study is made under the hypothesis that only the output data are corrupted by measurement errors. The main result of this paper is a proof that the variance of the impulsive response samples diverges when the sampling time tends toward zero.