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

TL;DR

This paper presents a new uncertainty principle for the short-time Fourier transform that challenges a specific conjecture and restricts certain signal profiles, providing insights into time-frequency analysis.

Contribution

It offers a negative answer to a question about the HRT conjecture and introduces a novel uncertainty principle for the short-time Fourier transform.

Findings

Negative answer to Kreisel's question regarding the HRT conjecture

New uncertainty principle restricts 'bump with fat tail' profiles

Provides theoretical insights into time-frequency analysis constraints

Abstract

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.