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Frequency-based methods have been successfully employed in creating highfidelity data-driven reduced order models (DDROMs) for linear dynamicalsystems. These methods require access to values (and sometimes derivatives) ofthe frequency-response function (transfer function) in the complex plane. Thesefrequency domain values can at times be costly or difficult to obtain(especially if the method of choice requires resampling); instead one may haveaccess to only time-domain input-output data. The data informativity approachto moment matching provides a powerful new framework for recovering therequired frequency data from a single time-domain trajectory. In this work, weanalyze and extend upon this framework, resulting in vastly improvedconditioning of the associated linear systems, an error indicator, and removalof an assumption that the system order is known. This analysis leads to arobust algorithm for recovering frequency information from time-domain data,suitable for large scale systems. We demonstrate the effectiveness of ouralgorithm by forming frequency based DDROMs from time-domain data of severaldynamical systems.

Frequency-Based Reduced Models from Purely Time-Domain Data via Data Informativity