Recent observations of auroral backscatter at frequencies from 10 to 933 MHz have found spectral shapes which are intermediate between Lorentzian and Gaussian. To account for these observations a model has been developed consisting of a random distribution of scatterers in the radar field of view. Spectral shape is discussed in terms of the shape of the magnitude of the temporal autocorrelation function (ACF--the Fourier transform of the spectrum), and within the assumptions of the model it is shown that the observed shapes arise from either the average ACF associated with the signal from individual scatterers or from the Doppler spread in the scattering volume. The observed spectral shapes are easily accounted for by a model for the individual scatterer signals consisting of an exponential growth, a quasi-steady section and an exponential decay.