Water-based dispersions and emulsions are used as model systems for a new rheological data analysis. The application of large amplitude oscillatory shear can be used to generate a high nonlinear response, which is analyzed by Fourier transform (FT)-rheology. The individual higher harmonics appearing in the shear stress response do not have a simple physical interpretation. Furthermore, in the FT analysis used so far the focus was mainly on the third harmonic relative to the fundamental I-3/I-1, even if multiple higher harmonics appear, as in the polystyrene dispersions examined here. As a consequence, we propose a new and simple method that considers the whole overtone spectra as a superposition of different overtone spectra of typical nonlinear rheological effects, like strain hardening, strain softening, and shear bands or wall slip. This novel analysis of FT-rheology experiments thus separates the nonlinear mechanical response into the underlying physical phenomena.