  Theoretical development and applications of graph signal processing (GSP)
have attracted much attention. In classical GSP, the underlying structures are
restricted in terms of dimensionality. A graph is a combinatorial object that
models binary relations, and it does not directly model complex n-ary
relations. One possible high dimensional generalization of graphs are
simplicial complexes. They are a step between the constrained case of graphs
and the general case of hypergraphs. In this paper, we develop a signal
processing framework on simplicial complexes, such that we recover the
traditional GSP theory when restricted to signals on graphs. It is worth
mentioning that the framework works much more generally, though the focus of
the paper is on simplicial complexes. We demonstrate how to perform signal
processing with the framework using numerical examples.
