  We establish a relation between Speh representations of
$\mathrm{GL}_n\left(\mathbb{F}_q\right)$ and Speh representations of
$\mathrm{GL}_n\left(F\right)$, where $F$ is a non-archimedean local field. We
use irreducible level zero supercuspidal representations to show that these two
notions of Speh representations associated to cuspidal representations are
related via a commutative diagram, and that their corresponding $(k,c)$
$\psi$-Whittaker models are also related. We use these results to relate the
local Ginzburg-Kaplan integrals for level zero supercuspidal representations to
their finite field counterparts.
