Compressor response investigation in nearly unstable operating conditions, like rotating stall and incipient surge, is a challenging topic nowadays in the turbomachinery research field. Indeed, turbines connected with large-size volumes are affected by critical issues related to surge prevention, particularly during transient operations. Advanced signal-processing operations conducted on vibrational responses provide an insight into possible diagnostic and predictive solutions which can be derived from accelerometer measurements. Indeed, vibrational investigation is largely employed in rotating-machine diagnostics together with time-frequency analysis such as smoothed pseudo-Wigner Ville (SPWVD) time-frequency distribution (TFD) considered in this paper. It is characterized by excellent time and frequency resolutions and thus it is effectively employed in numerous applications in the condition monitoring of machinery. The aim and the innovation of this work regards SPWVD utilization to study turbomachinery behavior in detail in order to identify incipient surge conditions in the centrifugal compressor starting from operational vibrational responses measured at significant plant locations. The so developed investigation allows us to assess the reliability of this innovative technique with respect to conventional ones in this field of research, highlighting at the same time its qualities and drawbacks in detecting fluid machinery unstable behavior. To this aim, an experimental campaign has been conducted on a T100 microturbine connected with several volume sizes and this has allowed to assess diagnostic technique reliability in plant configurations with different dynamic properties. The results show that SPWVD is able to successfully identify system evolution toward an unstable condition, by recognizing different levels and features of the particular kind of instability that is going to take place within the plant. Instability phenomena regarding rolling bearings have also been identified and their interaction with surge onset has been investigated for diagnostic purposes.