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

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 $\mathrm{\Lambda }=M{Z}^{2n}$ where M is a positive definite symmetric matrix.