cooling and heating of the IGM). In the extreme case that the transition from a fully neutral to a fully ionized IGM was virtually instantaneous, such that $\dot{\bar{x}}_{HI}(z_r)\rightarrow\infty$, where $z_r$ is the redshift of reionization, the contribution to the global spectrum at the frequencies corresponding to the reionization epoch would approach a step function. A sharp feature resembling a step function that is superimposed on the smooth power-law-like foreground spectrum should be relatively easy to identify. And if reionization were to progress more slowly, producing a smooth transition that spanned a large range of redshifts and many tens of MHz, a simple model could be used to set limits on the maximum rate of the transition.

In principle, a variety of such models could be devised to use in tests for the presence of a step feature in the radio spectrum due to a rapid reionization. A simple low-order polynomial fit to the measured spectrum would reveal such a discontinuous feature in the residual spectrum after subtracting the fit and, thus, would be able to determine the redshift range of a rapid reionization. Figure \[f\_edges\_model\] illustrates this approach by plotting a model (described in Section \[s\_edges\_limits\]) of the redshifted 21 