Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines.Here, we present a novel approach, based on the Hilbert transform (HT).We show that temporal periodicity can be uncovered by averagingthe signal in a moving window of appropriated length,t, before applying the HT. As a case study, we investigate global gridded surface airtemperature (SAT) datasets. By analyzing the variation of the mean rotation period,T, of the Hilbert phase as a function oft, we discoverwell-de ned plateaus. In many geographical regions, the plateau corresponds to the expected 1-yr solar cycle; however, in regions where SATdynamics is highly irregular, the plateaus reveal non-trivial periodicities, which can be interpreted in terms of climatic phenomena such asEl Niño. In these regions, we also nd that Fourier analysis is unable to detect the periodicity that emerges whentincreases and graduallywashes out SAT variability. The values ofTobtained for di erentts are then given to a standard machine learning algorithm. The resultsdemonstrate that these features are informative and constitute a new approach for SAT time series classi cation. To support these results, weanalyze the synthetic time series generated with a simple model and con rm that our method extracts information that is fully consistent withour knowledge of the model that generates the data. Remarkably, the variation ofTwithtin the synthetic data is similar to that observed in thereal SAT data. This suggests that our model contains the basic mechanisms underlying the unveiled periodicities. Our results demonstrate thatHilbert analysis combined with temporal averaging is a powerful new tool for discovering hidden temporal regularity in complex oscillatorysignals.