A system is described for time synchronizing digitized measurement signals, such as vibration signals. The digitized signals, which are acquired asynchronously by multiple distributed measurement units, indicate the operational condition of a machine or a process. To measure the phase of the digitized signals relative to a pulse tachometer input, the time between the leading edge of the tachometer pulse and the digitized samples is measured. To achieve phase-coherent synchronization across the distributed measurement units, a local synchronization signal is embedded into the data produced by the measurement units. The systems uses the synchronization signal to align the data in post processing, which phase aligns the data and aligns the data in absolute time. The synchronization signal may be encoded with a timestamp to provide additional timing information.