  Let $N$ be a non-commutative, simply connected, connected, two-step nilpotent
Lie group with Lie algebra $\mathfrak{n}$ such that $\mathfrak{n=a\oplus
b\oplus z}$, $\left[ \mathfrak{a},\mathfrak{b}\right] \subseteq \mathfrak{z},$
the algebras $\mathfrak{a},\mathfrak{b,z}$ are abelian,
$\mathfrak{a}=\mathbb{R}\text{-span}\left\{ X_{1},X_{2},\cdots,X_{d}\right\} ,$
and $\mathfrak{b}=\mathbb{R}\text{-span}\left\{ Y_{1},Y_{2},\cdots
,Y_{d}\right\} .$ Also, we assume that $\det\left[ \left[ X_{i}% ,Y_{j}\right]
\right] _{1\leq i,j\leq d}$ is a non-vanishing homogeneous polynomial in the
unknowns $Z_{1},\cdots,Z_{n-2d}$ where $\left\{ Z_{1},\cdots,Z_{n-2d}\right\} $
is a basis for the center of the Lie algebra. Using well-known facts from
time-frequency analysis, we provide some precise sufficient conditions for the
existence of sampling spaces with the interpolation property, with respect to
some discrete subset of $N$. The result obtained in this work can be seen as a
direct application of time-frequency analysis to the theory of nilpotent Lie
groups. Several explicit examples are computed. This work is a generalization
of recent results obtained for the Heisenberg group by Currey, and Mayeli in
\cite{Currey}.
