Ambient vibration modal identification, also known as Operational Modal Analysis (OMA), aims to identify the modal properties of a structure based on vibration data collected when the structure is under its operating conditions, i.e., when there is no initial excitation or known artificial excitation. This method for testing and/or monitoring historical buildings and civil structures, is particularly attractive for civil engineers concerned with the safety of complex historical structures. However, in practice, not only records of external force are missing, but uncertainties are involved to a significant extent. Hence, stochastic mechanics approaches are needed in combination with the identification methods to solve the problem. In this context, this paper’s contribution is to introduce an innovative ambient identification method based on the Hilbert Transform to obtain the analytical representation of the system response in terms of the correlation function. This approach opens the pathway for a monitoring system that is user friendly and can be used by people who have little to no knowledge of signal processing and stochastic analysis such as those who are responsible for the maintenance of a city’s historical buildings. In order to prove the reliability of the method several numerical examples and an experimental test are reported.