  A Wilson system is a collection of finite linear combinations of time
frequency shifts of a square integrable function. In this paper we use the fact
that a Wilson system is a shift-invariant system to explore its relationship
with Gabor systems. It is well known that, starting from a tight Gabor frame
for $L^{2}(\mathbb{R})$ with redundancy $2$, one can construct an orthonormal
Wilson basis for $L^{2}(\mathbb{R})$ whose generator is well localized in the
time-frequency plane. In this paper, we show that one can construct
multi-dimensional orthonormal Wilson bases starting from tight Gabor frames of
redundancy $2^k$ where $k=1, 2, ..., d$. These results generalize most of the
known results about the existence of orthonormal Wilson bases.
