Radio spectra of radio galaxies are often ascribed a simple power law form ( S _ { \nu } \propto \nu ^ { \alpha } ) with the spectral index , \alpha , being of order -0.7 .
However , all radio galaxies deviate from this simple power law behaviour .
In this paper we derive simple expressions for the average rest-frame spectra of FRI and FRII radio galaxies .
These will be used to describe the spectral curvature of the parent ( FRI and FRII ) populations in models of radio source evolution .