Powerful spectroscopic techniques increasingly involve nonlinear processes that arise due to the convolution of more than one electric field - input laser pulse. Analyzing the output of optical processes like these demands the utilization of deterministic improvement tools. Three-color coherent Raman scattering represents a complex non-degenerate four wave mixing process that includes contributions from both resonant and non-resonant interaction of the three input fields to generate a signal. In order to quantify these contributions, effective differentiation of the non- resonant (background) from the resonant (coherent signal) is required. These contributions can be differentiated based on how the molecular vibrational modes are being excited by the input pulses. The work described here demonstrates the ability of second-order correlation spectroscopy, applied along with an all-Gaussian theoretical model to analyze three color coherent Raman scattering processes. It is shown to discriminate between resonant versus non-resonant four wave mixing processes successfully. A robust, femtosecond/picosecond coherent Raman spectroscope is used to observe how the resonant signal builds up in a finite amount of time for different specimens and how it is can be controlled by input laser pulse shaping. A closed-form solution obtained via an all-Gaussian approach provides confirmatory theoretical proof of the experimental results obtained. This technique is used to study hydrogen bonding, which is a vital molecular interaction for bio-molecular systems and yet lacks a profound understanding of its ways of forming complexes. Furthermore, a novel second-order one-dimensional correlation function is introduced that replicates the results of the diagonal sum of the traditional synchronous two- dimensional correlation function, thus reducing a two-dimensional analysis to one-dimension. Along with the first demonstration of these analyses for coherent Raman scattering, a generalized approach is described, which opens up research opportunities to investigate these optical processes' dependence on multiple controlling parameters.