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arXiv · 1509.01437

Explicit construction of non-stationary frames for $L^2$

Ubertino Battisti·Michele Berra
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Abstract

We show the existence of a family of frames of $L^2(\mathbb{R})$ which depend on a parameter $\alpha\in [0,1]$. If $\alpha=0$, we recover the usual Gabor frame, if $\alpha=1$ we obtain a frame system which is closely related to the so called DOST basis, first introduced by Stockwell and then analyzed by Battisti and Riba. If $\alpha\in (0,1)$, the frame system is associated to a so called $\alpha$-partitioning of the frequency domain. Restricting to the case $\alpha=1$, we provide a truly $n$-dimensional version of the DOST basis and an associated frame of $L^2(\mathbb{R}^d)$.

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Ubertino Battisti, Michele Berra. 2015-09-04. Explicit construction of non-stationary frames for $L^2$. https://arxiv.org/abs/1509.01437

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