Measurements of the highly redshifted 21-cm line promise to provide a great deal of information about the dark ages of the Universe, the cosmic dawn and the epoch of reionization. It is generally accepted that strong astrophysical foregrounds are a major obstacle to overcome before this promise is realised, largely because of the way they are filtered through a complicated instrumental response. A great deal of work has therefore been devoted to studying foreground removal for observations with the low-frequency radio arrays which are starting to collect data. The case of so-called 'global signal' experiments has received less attention, however. I will compare the foreground fitting problem in these two types of experiments, and describe a foreground fitting methodology which has been developed for a proposed global signal experiment, the Dark Ages Radio Explorer. This will be applicable more generally to other space- and ground-based experiments.