Coherent continuous wave (CW) terahertz spectroscopy is an extremely valuable technique that allows for the interrogation of systems that exhibit narrow resonances in the terahertz (THz) frequency range, such as high-quality (high-Q) THz whispering-gallery mode resonators. Unfortunately, common implementations are dramatically impaired by deficiencies in the used data analysis schemes. Here, we show that the physics of the problem presents an elegant solution whose full potential has remained overlooked until now. We argue that, thanks to the causality of physical systems, Hilbert transformation can be used to analyze the frequency response of linear systems with arbitrarily narrow resonance features in coherent CW THz spectroscopy. In particular, by establishing that signals encountered in typical experiments are closely related to analytic signals, we demonstrate that Hilbert transformation is applicable even when the envelope varies rapidly compared to the oscillation period.
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