An approach to estimate time-varying casual coherence function

This paper describes the development of a model-based approach to estimating both open-loop and causal time-varying coherence functions (TVCF). Theoretical derivations of the coherence bounds using the proposed approach are also provided.

A time-varying vector autoregressive (VAR) model was used to estimate both open-loop and causal TVCF. The time-varying optimal parameter search method was employed to identify the time-varying model coefficients as well as the model order of the VAR model.

Simulation results revealed interesting observations, and they were corroborated using experimental renal blood pressure and flow data. Specifically, experimental data showed that in certain cases, the calculation of the open-loop TVCF might provide incorrect interpretation of the results when the system under investigation was a closed-loop system, which is consistent with theoretical derivations.

The use of the closed-loop TVCF not only provides quantitative assessment of the coupling between the two signals, but it also provides valuable insights into the composition of the physical structure of the system.