  In this paper we consider the problem of constructing graph Fourier
transforms (GFTs) for directed graphs (digraphs), with a focus on developing
multiple GFT designs that can capture different types of variation over the
digraph node-domain. Specifically, for any given digraph we propose three GFT
designs based on the polar decomposition. Our method is closely related to
existing polar decomposition based GFT designs, but with added interpretability
in the digraph node-domain. Each of our proposed digraph GFTs has a clear node
domain variation interpretation, so that one or more of the GFTs can be used to
extract different insights from available graph signals. We demonstrate the
benefits of our approach experimentally using M-block cyclic graphs, showing
that the diffusion of signals on the graph leads to changes in the spectrum
obtained from our proposed GFTs, but cannot be observed with the conventional
GFT definition.
