"Velocity in fourier space" refers to the discrete fourier transformation of the spatial coordinates of the velocities of a MPC fluid's constituents. The corresponding formula is given by

\[ \vec{v}\left(\vec{k}, t\right) = \frac{1}{N} \sum_{i=1}^N \vec{v}_i\left(t\right) \cdot \exp\left( \mathrm{i} \vec{k} \cdot \vec{r}_i\left(t\right) \right) \]

See, for example, "Hydrodnymic correlations in multiparticle collision dynamics" by Chien-Cheng Huang, Gerhard Gompper, and Roland G. Winkler, published in Physical Review E 86, 056711 (2012), equation (38).