Sleep spindles occur thousands of times during normal sleep and can be easily detected by visual inspection of EEG signals. These characteristics make spindles one of the most studied EEG structures in mammalian sleep. In this work we considered global spindles, which are spindles that are observed simultaneously in all EEG channels. We propose a methodology that investigates both the signal envelope and phase/frequency of each global spindle. By analysing the global spindle phase we showed that 90% of spindles synchronize with an average latency time of 0.1 s. We also measured the frequency modulation (chirp) of global spindles and found that global spindle chirp and synchronization are not correlated. By investigating the signal envelopes and implementing a homogeneous and isotropic propagation model, we could estimate both the signal origin and velocity in global spindles. Our results indicate that this simple and non-invasive approach could determine with reasonable precision the spindle origin, and allowed us to estimate a signal speed of 0.12 m/s. Finally, we consider whether synchronization might be useful as a non-invasive diagnostic tool.