We analyze the cut-off dependence of mesonic spectral functions calculated at finite temperature on Euclidean lattices with finite temporal extent. In the infinite temperature limit we present analytic results for lattice spectral functions calculated with standard Wilson fermions as well as a truncated perfect action. We explicitly determine the influence of `Wilson doublers on the high momentum structure of the mesonic spectral functions and show that this cut-off effect is strongly suppressed when using an improved fermion action.
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