Tight frames generated by a graph short-time Fourier transform

Abstract

A graph short-time Fourier transform is defined using the eigenvectors of the graph Laplacian and a graph heat kernel as a window parametrized by a nonnegative time parameter t. We show that the corresponding Gabor-like system forms a frame for $C^d$ and gives a description of the spectrum of the corresponding frame operator in terms of the graph heat kernel and the spectrum of the underlying graph Laplacian. For two classes of algebraic graphs, we prove the frame is tight and independent of the window parameter t.