A common model for the photodissociative potential surfaces of the triiodide ion in ethanol is used to simulate both the spontaneous resonance Raman (RR) spectra and the femtosecond resonant impulsive stimulated Raman scattering (RISRS) signals for comparison with experimental data. The Fourier transforms of the RISRS signals, while resembling RR spectra, are not the same either theoretically or experimentally, and these differences are only partly due to the finite spectral bandwidth of the pulses in the RISRS experiment. The RISRS signals vary much more strongly with wavelength than do the RR spectra. Direct Fourier transformation of the RISRS signals with a fixed phase tends to diminish the apparent contributions of weaker components due to the different phases of different oscillations. Linear prediction singular value decomposition (LPSVD) is shown to give a more faithful representation of the RISRS power spectra by eliminating the phase problem, but there are still significant differences between the RR and LPSVD-RISRS spectra. Our model, which includes a large number of combination bands between triiodide vibrations and a low frequency solvent or intermolecular mode, gives a good representation of both the experimental RR profiles and the 308 nm RISRS data of Banin et al. [U. Banin, R. Kosloff, and S. Ruhman, Isr. J. Chem 33, 141 (1893)].