We propose an explanation for large discrepancies in the absorption spectrum of a-Si:H between measurements by DC and AC constant photocurrent methods (CPM). DC measurement gives a consistently higher value for the absorption coefficient a at low photon energies. A small-signal analysis of the photoconductive response to modulated sub-gap illumination reveals low frequency poles associated with thermal emission processes, which explain this discrepancy. We demonstrate with computer simulations that while DC CPM, which includes these transitions, gives a more accurate value for absorption, AC CPM provides a more accurate means of determining the distribution of occupied gap-states. Further, we show that combining DC and AC methods allows determination of the distribution of deep unoccupied gap-states. These concepts are applied to experimental results for several undoped a-Si:H films.