We establish a statistical-measures approach to describe the spectral-spatial analysis of the dynamical atom-field couplings associated with two-pair of pulses propagation in multilevel atomic media. The statistical measures are functional measures that depend on the collective coupling as well as on the eigenvalues of the Nonlinear-Liouville equation. The Nonlinear-Liouville equation is a nonlinear evolution equation which is a second-order differential equation in time. It describes the multi-wave mixing process within the atomic system, as well as coherent oscillations. The proposed spectral estimators prevail spatial multi-peak structure, which depends on the reduction or the enhancement of an effective Rabi-frequency. Decomposition of collective oscillations provides an intuitive guess to special-weight of the field's area. We introduce two functional wavelets to simulate the atomic polarization response. One of these functionals exposes the dependence on the multicomponent sine-Gordon equation for the atomic polarization, which is adequate at relatively small propagation distances. The second one is composed of combined sine and cosine functionals on the area of the fields. The cosine functional reflects the significance of the atomic inversion on the polarization response to electromagnetic field excitations. The proposed functional-wavelets inducts new sources for soliton features to the transition-radiation propagation associated with Maxwell-Bloch equations.