  The broad-bandwidth capabilities of next generation telescopes such as the
JVLA mean that the spectrum of any given source varies significantly within the
bandwidth of any given observation. Detailed spectral analysis taking this
variation into account is set to become standard practice when dealing with any
new broadband radio observations; it is therefore vital that methods are
developed to handle this new type of data. In this paper, we present the
Broadband Radio Astronomy ToolS (BRATS) software package and, use it to carry
out detailed analysis of JVLA observations of three powerful radio galaxies. We
compare two of the most widely used models of spectral ageing, the
Kardashev-Pacholczyk and Jaffe-Perola models and also results of the more
complex, but potentially more realistic, Tribble model. We find that the
Tribble model provides both a good fit to observations as well as providing a
physically realistic description of the source. We present the first
high-resolution spectral maps of our sources and find that the best-fitting
injection indices across all models take higher values than has previously been
assumed. We present characteristic hot spot advance speeds and make comparison
to those derived from dynamical ages, confirming the previously known
discrepancy in speed remains present when determined at high spectral
resolutions. We show that some previously common assumptions made in
determining spectral ages with narrow-band radio telescopes may not always hold
and strongly suggest these are accounted for in future investigations.
