Distributed edge-variant graph filters

The main challenges distributed graph filters face in practice are the communication overhead and computational complexity. In this work, we extend the state-of-the-art distributed finite impulse response (FIR) graph filters to an edge-variant (EV) version, i.e., a filter where every node weights the signals from its neighbors with different values. Besides having the potential to reduce the filter order leading to amenable communication and complexity savings, the EV graph filter generalizes the class of classical and node-variant FIR graph filters. Numerical tests validate our findings and illustrate the potential of the EV graph filters to (i) approximate a user-provided frequency response; and (ii) implement distributed consensus with much lower orders than its direct contenders.