A Characterization of Multivariate Gaussian Weyl--Heisenberg Frames, (II)

TL;DR

This paper extends the characterization of multivariate Gaussian Weyl--Heisenberg frames to more general lattice structures, broadening the understanding of when such systems form frames in signal analysis.

Contribution

It generalizes previous results by establishing frame conditions for lattices defined by positive definite matrices, beyond rectangular lattices.

Findings

Extended frame characterization to lattices of the form MZ^{2n}.

Provided necessary and sufficient conditions for these generalized Weyl--Heisenberg systems.

Broadened the applicability of Gaussian frames in multivariate analysis.

Abstract

In a previous Note we established a necessary and sufficient condition for a multivariate Weyl--Heisenberg system G({\phi},{\Lambda}) to be a frame when the window is a generalized Gaussian (squeezed coherent state) and {\Lambda} a rectangular lattice. In this Note we extend this result to lattices of the type ${\Lambda}=MZ^{2n}$ where M is a positive definite symmetric matrix.