Output Linear Time Invariant Systems Research Articles

Online adaptive identification of multichannel systems for audio applications.

Impulse responses (IRs) estimation of multi-input acoustic systems is a prerequisite for many audio applications. In this paper, an adaptive identification problem based on the Autostep algorithm is extended to the simultaneous estimation of room IRs for multiple input single output linear time invariant systems without any a priori information. To do so, the proposed algorithm is initially evaluated in a simulated room with several sound sources active at the same time. Finally, an experimental validation is proposed for the cases of a semi-anechoic chamber and an arbitrary room. Special attention is dedicated to the algorithm convergence behavior, considering different meta parameters settings. Results are eventually compared with the other normalized version of the least mean square algorithm.

On cross-correlogram IRF’s estimators of two-output systems in spaces of continuous functions

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 L 2-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.

Adaptive Input Design for LTI Systems

Optimal input design for parameter estimation has obtained extensive coverage in the past. A key problem here is that the optimal input depends on some unknown system parameters that are to be identified. Adaptive design is one of the fundamental routes to handle this problem. Although there exist a rich collection of results on this problem, there are few results that address dynamical systems. This paper presents sufficient conditions for convergence/consistency and asymptotic optimality for a class of adaptive systems consisting of a recursive prediction error estimator and an input generator depending on the time-varying parameter estimates. The results apply to a general family of single input single output linear time-invariant systems. An important application is adaptive input design for which the results imply that, asymptotically in the sample size, the adaptive scheme recovers the same accuracy as the off-line prediction error method that uses data from an experiment where perfect knowledge of the system has been used to design an optimal input spectrum.