Femtosecond transient absorption spectra of molecules in solution change when an ultrafast reaction creates a new product state, and coherent optical processes complicate the spectra during the pump pulse. A low frequency vibration may also be found to modulate an absorption or emission band for the first few picoseconds. For singular value decomposition of the data one identifies the educt, intermediate. and product states by their temporal behavior and thereby determines the spectra associated with these photochemical species. Here we extend this method by introducing two additional "species": the apparatus function and the low-frequency oscillation. Associated with the apparatus function is the coherent spectrum. The spectrum of oscillations is obtained directly by optimizing a generalized rotation matrix, without need of model functions. It consists of band derivatives times oscillation amplitudes and after integration assists in decomposing the transient absorption spectra. The method is demonstrated with the excited-state intramolecular proton transfer (ESIPT) reaction of 2.5-bis(2'-benzoxazolyl)hydroquinone in tetrahydrofuran. Ultrafast optical pumping prepares the excited enol form of the molecule. Its blue stimulated emission band prior to the reaction is reported for the first time. The enol form reacts with 110 +/- 15 fs time constant to the excited keto form which emits in the red. The latter is created with coherent excitation of an H-chelate-ring bending vibration of 118 cm(-1) and the proton transfer occurs during the first half-cycle. The wave packet modulates the frequency for an excited-state absorption (ESA) band of the keto form and for its stimulated emission band, with initial frequency excursions of +130 cm(-1) and -180 cm(-1), respectively. The dominant ESA band is extracted quantitatively from the data. Intramolecular vibrational redistribution in the excited keto state is characterized by vibrational dephasing (0.89 +/- 0.1 p.s time constant) and a red shift of the ESA band (1.26 +/- 0.1 ps). The spectra of all species are obtained and decomposed.