Wild character varieties are spaces of monodromy data for irregular connections on a curve. On $\mathbb{P}^1$, the purity conjecture of Hausel-Rodriguez-Villegas identifies the pure part of their cohomology with the cohomology of the so-called open de Rham space through the Riemann-Hilbert map. In this talk I will provide evidence for this conjecture by computing the motivic classes of open de Rham spaces using a Fourier transform on Grothendieck rings. This is joint work with Tamas Hausel and Michael Wong.