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

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.