# Filter Design for Autoregressive Moving Average Graph Filters

arXiv: https://arxiv.org/abs/1711.09086 · HTML: https://mlsanity.com/paper/1711.09086/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2017.

## Built on by (most cited first, 8 of 8)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Beyond Low-Pass Filters: Adaptive Feature Propagation on Graphs](https://mlsanity.com/paper/2103.14187/) (2021)
- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Learning Optimal Graph Filters for Clustering of Attributed Graphs](https://mlsanity.com/paper/2211.04634/) (2022)
- [Learning Graph Filters for Structure-Function Coupling based Hub Node Identification](https://mlsanity.com/paper/2410.17410/) (2024)
- [Locally Stationary Graph Processes](https://mlsanity.com/paper/2309.01657/) (2023)
- [Joint Data Inpainting and Graph Learning via Unrolled Neural Networks](https://mlsanity.com/paper/2407.11429/) (2024)
- [TwinS-GCN: Spectral conjugate for Spectral Graph Convolutional Networks](https://mlsanity.com/paper/2609.32940/) (2026)

## Abstract (arXiv)

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.