It is shown here that a simple weighted average dielectric function describes the experimental infrared reflection/absorption spectra of titanium oxide films with a granular nanostructure. The films were grown on unheated substrates by reactive sputter deposition using a Ti metal target and a 10 mTorr pure O-2 discharge. The films' average dielectric function is derivable from a Maxwell-Garnett model in which randomly oriented nanograins with anatase short-range atomic order are embedded in a conducting background. In contrast, dielectric functions calculated using effective-medium and Maxwell-Garnett theories that do not consider the background fail to adequately account for the experimental absorption peak positions. High-resolution transmission electron microscopy confirmed the films' granular nanostructure and the presence of Ti suboxides as a minority constituent. We associate the anatase-like constituent with the model's embedded grains, and the Ti suboxide constituent with the model's background medium. The formalism that is developed here is applicable to any composite system consisting of grains embedded in a medium whose dielectric function is much larger than that of the grains. (C) 2004 American Vacuum Society.