Proof of the HRT conjecture for almost every (1,3) configuration

TL;DR

This paper proves the HRT conjecture for almost every (1,3) configuration, demonstrating that for most such configurations, the associated time-frequency translates of any non-zero function are linearly independent.

Contribution

It extends the proof of the HRT conjecture to almost all (1,3) configurations, building on Demeter's previous work.

Findings

HRT conjecture holds for almost every (1,3) configuration

Linear independence of time-frequency translates is established in these cases

Supports the conjecture's validity in a broad class of configurations

Abstract

Based on the proof of Demeter \We prove that for almost every (1,3) configuration, there is no linear dependence between the associated time-frequency translates of any $f\in L^2(\R)\backslash \{0\}$.cite{Dem10}, we establish the HRT conjecture for almost every (1,3) configuration.