  We present new low-frequency observations of the nearby radio galaxy Fornax A
at 154 MHz with the Murchison Widefield Array, microwave flux-density
measurements obtained from WMAP and Planck data, and gamma-ray flux densities
obtained from Fermi data. We also compile a comprehensive list of previously
published images and flux-density measurements at radio, microwave and X-ray
energies. A detailed analysis of the spectrum of Fornax A between 154 MHz and
1510 MHz reveals that both radio lobes have a similar spatially-averaged
spectral index, and that there exists a steep-spectrum bridge of diffuse
emission between the lobes. Taking the spectral index of both lobes to be the
same, we model the spectral energy distribution of Fornax A across an energy
range spanning eighteen orders of magnitude, to investigate the origin of the
X-ray and gamma-ray emission. A standard leptonic model for the production of
both the X-rays and gamma-rays by inverse-Compton scattering does not fit the
multi-wavelength observations. Our results best support a scenario where the
X-rays are produced by inverse-Compton scattering and the gamma-rays are
produced primarily by hadronic processes confined to the filamentary structures
of the Fornax A lobes.
