In the field of signal processing on graphs, graph filters play a crucialrole in processing the spectrum of graph signals. This paper proposes twodifferent strategies for designing autoregressive moving average (ARMA) graphfilters on both directed and undirected graphs. The first approach is inspiredby Prony's method, which considers a modified error between the modeled and thedesired frequency response. The second technique is based on an iterativeapproach, which finds the filter coefficients by iteratively minimizing thetrue error (instead of the modified error) between the modeled and the desiredfrequency response. The performance of the proposed algorithms is evaluated andcompared with finite impulse response (FIR) graph filters, on both syntheticand real data. The obtained results show that ARMA filters outperform FIRfilters in terms of approximation accuracy and they are suitable for graphsignal interpolation, compression and prediction.
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