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arXiv · 2608.05044

Linear dependence of time-frequency shifts of a Schwartz function

Markus Faulhuber·Philipp Petersen·Jordy Timo van Velthoven·Felix Voigtlaender
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Abstract

We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwala. In particular, we provide an example consisting of 12 time-frequency shifts.

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Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven, Felix Voigtlaender. 2026-08-05. Linear dependence of time-frequency shifts of a Schwartz function. https://arxiv.org/abs/2608.05044

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