A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform

A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform

In this note we provide a negative answer to a question raised by M. Kreisel concerning a condition on the short-time Fourier transform that would imply the HRT conjecture. In particular we provide a new type of uncertainty principle for the short-time Fourier transform which forbids the arrangement...

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Veröffentlicht in:arXiv.org 2019-11
Hauptverfasser: Nicola, Fabio, Trapasso, S Ivan
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Fourier transforms
Mathematics - Classical Analysis and ODEs
Mathematics - Functional Analysis
Uncertainty principles
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description In this note we provide a negative answer to a question raised by M. Kreisel concerning a condition on the short-time Fourier transform that would imply the HRT conjecture. In particular we provide a new type of uncertainty principle for the short-time Fourier transform which forbids the arrangement of an arbitrary "bump with fat tail" profile.
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subjects Fourier transforms
Mathematics - Classical Analysis and ODEs
Mathematics - Functional Analysis
Uncertainty principles
title A note on the HRT conjecture and a new uncertainty principle for the short-time Fourier transform
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