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In this article, single input–double output linear time-invariant systems are studied. Both components of system's impulse response function are supposed to be real-valued and L2-integrable. One component is unknown while the second one is controlled. The problem is to estimate the unknown component after observations of the other component. For this purpose, we apply cross-correlating of the outputs given that the input is a standard Wiener process on R. Weak asymptotic normality of appropriately centered estimators in spaces of continuous functions is proved. This enables us to construct confidence intervals in these spaces. Our results employ techniques related to Gaussian processes and bilinear forms of Gaussian processes. [ABSTRACT FROM AUTHOR]

A single input–double output (SIDO) linear time-invariant (LTI) system is considered, whose impulse response function (IRF) is assumed to have one unknown component. The problem is to estimate this unknown component after observations of the second component. Both IRF's components are supposed to be L2-integrable, and the estimation is made by cross-correlating the outputs, given that the input is a standard Wiener process on R. Weak asymptotic normality of appropriately centred estimators is proved. [ABSTRACT FROM AUTHOR]

Proves the asymptotic normality of the sample correlogram of a stationary Gaussian process in the space of continuous real-valued functions. Theorems on asymptotic normality of the sample correlogram; Discussion on the theory of Gaussian random functions; Proofs of the theorems.