  In the field of signal processing on graphs, graph filters play a crucial
role in processing the spectrum of graph signals. This paper proposes two
different strategies for designing autoregressive moving average (ARMA) graph
filters on both directed and undirected graphs. The first approach is inspired
by Prony's method, which considers a modified error between the modeled and the
desired frequency response. The second technique is based on an iterative
approach, which finds the filter coefficients by iteratively minimizing the
true error (instead of the modified error) between the modeled and the desired
frequency response. The performance of the proposed algorithms is evaluated and
compared with finite impulse response (FIR) graph filters, on both synthetic
and real data. The obtained results show that ARMA filters outperform FIR
filters in terms of approximation accuracy and they are suitable for graph
signal interpolation, compression and prediction.
