On Wilson Bases in L2(ℝd)

A Wilson system is a collection of finite linear combinations of time frequency shifts of a square integrable function. It is well known that, starting from a tight Gabor frame for L2(R) with redundancy 2, one can construct an orthonormal Wilson basis for L2(R) whose generator is well localized in the time-frequency plane. In this paper we use the fact that a Wilson system is a shiftinvariant system to explore its relationship with Gabor systems. Specifically, we show that one can construct d-dimensional orthonormal Wilson bases starting from tight Gabor frames of redundancy 2k, where k = 1, 2, . . . , d. These results generalize most of the known results about the existence of orthonormal Wilson bases.

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