Estimation of impulse response functions in two-output systems

Abstract

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.

Keywords:

• Linear time-invariant system
• impulse response function
• cross-correlogram
• cumulant
• central limit theorem

Acknowlegements

This work was partially supported by the MINECO/FEDER under Grant MTM2015-69493-R. The first author would like to thank Professors Puig-Casado and del Castillo-Franquet for their hospitality during her research stay at the Universitat Autònoma de Barcelona. The authors would like to thank an anonymous referee for a careful reading of the manuscript and for suggested modifications that have improved the paper.

Additional information

Funding

Secretaría de Estado de Investigación, Desarrollo e Innovación.