Simplicial Convolutional Filters

We study linear filters for processing signals supported on abstract topological spaces modeled as simplicial complexes, which may be interpreted as generalizations of graphs that account for nodes, edges, triangular faces, etc. To process such signals, we develop simplicial convolutional filters defined as matrix polynomials of the lower and...

Finite Impulse Response Filters for Simplicial Complexes

In this paper, we study linear filters to process signals defined on simplicial complexes, i.e., signals defined on nodes, edges, triangles, etc. of a simplicial complex, thereby generalizing filtering operations for graph signals. We propose a finite impulse response filter based on the Hodge Laplacian, and demonstrate how this filter can be...