We have applied the recently demonstrated exponential mode expansion method to the velocity autocorrelation function (VAF), a key quantity in the atomic-scale dynamics of fluids that has provided the first paradigmatic example of a long-time tail phenomenon. The new approach shows that there is much more to the VAF than simply the evidence of this long-time dynamics and allows for a full account and understanding of the basic dynamical processes encompassed by the VAF. By consistently exploiting the interpretation of its frequency spectrum as a global density of states in the fluid, we assign specific and unambiguous physical meanings to groups of modes related to the longitudinal and transverse collective dynamics, respectively. The high-frequency oscillating component of the VAF is then clearly related to acoustic waves. As for the transverse modes, the multi-exponential expansion reveals a transition marking the onset of propagating excitations when the density is increased beyond a threshold value, a result in agreement with the recent literature debating the issue of dynamical crossover boundaries such as the Frenkel line. This will also help obtain a still missing full account of transverse dynamics, in both its nonpropagating and propagating aspects which are linked through dynamical transitions depending on both the thermodynamic states and the excitation wavevectors.