  Willems' fundamental lemma has recently received an impressive amount of
attention in the (data-driven) control community. In this paper, we formulate a
frequency-domain equivalent of this lemma. In doing so, we bridge the gap
between recent developments in data-driven analysis and control and the
extensive knowledge on non-parametric frequency-domain identification that has
accumulated, particularly in industry, through decades of working with
classical (frequency-domain) control and identification techniques. Our
formulation also allows for the combination of multiple data sets in the sense
that, in the data, multiple input directions may be excited at the same
frequency. We also illustrate the usefulness of our results by demonstrating
how they can be applied to perform frequency-domain-data-driven simulation.
