Metaplectic Quantum Time--Frequency Analysis, Operator Reconstruction and Identification

TL;DR

This paper explores operator identification and reconstruction within Quantum Time--Frequency Analysis using metaplectic geometry, focusing on discretising the diagonal of the polarised Cohen's class for accurate operator analysis.

Contribution

It introduces a novel framework leveraging metaplectic geometry for operator reconstruction from Gabor matrix diagonals in Quantum Time--Frequency Analysis.

Findings

Operators can be reconstructed from Gabor matrix diagonals using the proposed framework.

Metaplectic geometry provides generalized conditions for operator identification.

The approach enables discretisation of the polarised Cohen's class for practical operator analysis.

Abstract

The problem of identifying and reconstructing operators from a diagonal of the Gabor matrix is considered. The framework of Quantum Time--Frequency Analysis is used, wherein this problem is equivalent to the discretisation of the diagonal of the polarised Cohen's class of the operator. Metaplectic geometry allows the generalisation of conditions on appropriate operators, giving sets of operators which can be reconstructed and identified on the diagonal of the discretised polarised Cohen's class of the operator.