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arXiv · 1703.08600

On Wilson bases in L2(R^d)

Marcin Bownik·Mads Sielemann Jakobsen·Jakob Lemvig·Kasso A. Okoudjou
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Abstract

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.

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Marcin Bownik, Mads Sielemann Jakobsen, Jakob Lemvig, Kasso A. Okoudjou. 2017-03-24. On Wilson bases in L2(R^d). https://arxiv.org/abs/1703.08600

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