Non-parametric best linear time invariant approximation of a linear time-varying system

The consequences of estimating the frequency response function of a continuous-time, linear time-varying (LTV) system with tools for linear time invariant (LTI) systems are studied. To this end, the best linear time invariant approximation of an LTV system is defined, and is related to a general model for LTV systems. A recently introduced frequency response function estimation method for LTI systems is used to compute the best linear time invariant approximation, the properties of which are discussed. An analysis of the residual error specifies whether the system under consideration is time-varying or not. Also, the frequency band where the contributions from the time variation are higher than the noise floor is determined. All concepts are illustrated on simulation examples.