  Graph Fourier transform (GFT) is one of the fundamental tools in graph signal
processing to decompose graph signals into different frequency components and
to represent graph signals with strong correlation by different modes of
variation effectively. The GFT on undirected graphs has been well studied and
several approaches have been proposed to define GFTs on directed graphs. In
this paper, based on the singular value decompositions of some graph
Laplacians, we propose two GFTs on the Cartesian product graph of two directed
graphs. We show that the proposed GFTs could represent spatial-temporal data
sets on directed networks with strong correlation efficiently, and in the
undirected graph setting they are essentially the joint GFT in the literature.
In this paper, we also consider the bandlimiting procedure in the spectral
domain of the proposed GFTs, and demonstrate its performance to denoise the
temperature data set in the region of Brest (France) on January 2014.
