Vibrational analysis in solution and the theoretical determination of infrared and Raman spectra are of key importance in many fields of chemical interest. Vibrational band dynamics of molecules and their sensitivity to the environment can also be captured by these spectroscopies in their time dependent version. However, it is often difficult to provide an interpretation of the experimental data at the molecular scale, such as molecular mechanisms or the processes hidden behind them. In this work, we present a theoretical-computational protocol based on ab initio molecular dynamics simulations and a combination of normal-like (generalized) mode analysis of solute-solvent clusters with a wavelet transform, for the first time. The case study is the vibrational dynamics of N-methyl-acetamide (NMA) in water solution, a well-known model of hydration of peptides and proteins. Amide modes are typical bands of peptide and protein backbone, and their couplings with the environment are very challenging in terms of the accurate prediction of solvent induced intensity and frequency shifts. The contribution of water molecules surrounding NMA to the composition of generalized and time resolved modes is introduced in our vibrational analysis, showing unequivocally its influence on the amide mode spectra. It is also shown that such mode compositions need the inclusion of the first shell solvent molecules to be accurately described. The wavelet analysis is proven to be strongly recommended to follow the time evolution of the spectra, and to capture vibrational band couplings and frequency shifts over time, preserving at the same time a well-balanced time-frequency resolution. This peculiar feature also allows one to perform a combined structural-vibrational analysis, where the different strengths of hydrogen bond interactions can quantitatively affect the amide bands over time at finite temperature. The proposed method allows for the direct connection between vibrational modes and local structural changes, providing a link from the spectroscopic observable to the structure, in this case the peptide backbone, and its hydration layouts.