When exciting a complex molecular system with a short optical pulse, all chromophores present in the system can be excited. The resulting superposition of electronically and vibrationally excited states evolves in time, which is monitored with transient absorption spectroscopy. We present a methodology to resolve simultaneously the contributions of the different electronically and vibrationally excited states from the complete data. The evolution of the excited states is described with a superposition of damped oscillations. The amplitude of a damped oscillation cos(ωnt)exp(−γnt) as a function of the detection wavelength constitutes a damped oscillation associated spectrum DOASn(λ) with an accompanying phase characteristic φn(λ). In a case study, the cryptophyte photosynthetic antenna complex PC612 which contains eight bilin chromophores was excited by a broadband optical pulse. Difference absorption spectra from 525 to 715 nm were measured until 1 ns. The population dynamics is described by four lifetimes, with interchromophore equilibration in 0.8 and 7.5 ps. We have resolved 24 DOAS with frequencies between 130 and 1649 cm−1 and with damping rates between 0.9 and 12 ps−1. In addition, 11 more DOAS with faster damping rates were necessary to describe the “coherent artefact.” The DOAS contains both ground and excited state features. Their interpretation is aided by DOAS analysis of simulated transient absorption signals resulting from stimulated emission and ground state bleach.