  Coherent Raman scattering spectroscopy is studied purposely, with the
Gaussian ultrashort pulses as a hands-on elucidatory extraction tool of the
clean coherent Raman resonant spectra from the overall measured data
contaminated with the non-resonant four wave mixing background. The integral
formulae for both the coherent anti-Stokes and Stokes Raman scattering are
given in the semiclassical picture, and the closed-form solutions in terms of a
complex error function are obtained. An analytic form of maximum enhancement of
pure coherent Raman spectra at threshold time delay depending on bandwidth of
probe pulse is also obtained. The observed experimental data for pyridine in
liquid-phase are quantitatively elucidated and the inferred time-resolved
coherent Raman resonant results are reconstructed with a new insight.
