  In this paper, we present a novel generalization of the graph Fourier
transform (GFT). Our approach is based on separately considering the
definitions of signal energy and signal variation, leading to several possible
orthonormal GFTs. Our approach includes traditional definitions of the GFT as
special cases, while also leading to new GFT designs that are better at taking
into account the irregular nature of the graph. As an illustration, in the
context of sensor networks we use the Voronoi cell area of vertices in our GFT
definition, showing that it leads to a more sensible definition of graph signal
energy even when sampling is highly irregular.
