  We determine the irregular Hodge filtration, as introduced by Sabbah, for the
purely irregular hypergeometric $\mathcal{D}$-modules. We obtain in particular
a formula for the irregular Hodge numbers of these systems. We use the
reduction of hypergeometric systems from GKZ-systems as well as comparison
results to Gauss-Manin systems of Laurent polynomials via Fourier-Laplace and
Radon transformations.
