In graph signal processing, signals are processed by explicitly taking into account their underlying structure, which is generally characterized by a graph. In this field, graph filters play a major role to process such signals in the so-called graph frequency domain. In this paper, we focus on the design of autoregressive moving average (ARMA) graph filters and basically present two design approaches. The first approach is inspired by Prony's method, which considers a modified error between the modeled and the desired frequency response. The second approach is based on an iterative method, 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 design algorithms is evaluated and compared with finite impulse response (FIR) graph filters. The obtained results show that ARMA filters outperform FIR filters in terms of approximation accuracy even for the same computational cost.@en

The ability to model irregular data and the interactions between them have extended the traditional signal processing tools to the graph domain. Under these circumstances, the emergence of graph signal processing has offered a brand new framework for dealing with complex data. In particular, the graph Fourier transform (GFT) lets us analyze the spectral components of a graph signal in the graph frequency domain. Based on the GFT, graph filters provide useful tools to modify or extract spectral parts in terms of different objectives, e.g., using a low-pass graph filter to construct graph signals without noise. This thesis mainly focuses on designing and implementing graph filters. Similar to traditional signal processing, we investigate two types of graph filters: finite impulse response (FIR) and infinite impulse response (IIR) graph filters. Moreover, this thesis takes both undirected and directed graphs into account for the design methods and implementations. @en

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.@en

Localization using received signal strength (RSS) measurements becomes popular due to the simplicity of practical implementation. Traditional RSS measurements are obtained after successful demodulation such that the impact of the background noise (BGN) is ignored. However, critical information for demodulation might be expensive or difficult to obtain in hostile or harsh environments. In this case, the RSS measurements need to be blindly collected without demodulation and hence characterized by a recent model with the BGN power (already validated by real-life data). This kind of measurement is referred to as 'blind RSS measurement'. In this letter, we introduce four models for the localization using the blind RSS measurements, respectively considering the BGN power and the transmit power to be known or unknown. A general semi-definite programming solution that applies to all these models is proposed. The corresponding Cramér-Rao lower bounds are presented, indicating a significant impact of the BGN power on the estimation accuracy. Numerical results show the proposed method yields a good and reliable performance with different models.@en

To accurately match a finite-impulse response (FIR) graph filter to a desired response, high filter orders are generally required leading to a high implementation cost. Autoregressive moving average (ARMA) graph filters can alleviate this problem but their design is more challenging. In this paper, we focus on ARMA graph filter design for a known graph. The fundamental aim of our ARMA design is to create a good match to the desired response but with less coefficients than a FIR filter. Our design methods are inspired by Prony’s method but using proper modifications to fit the design to the graph context. Compared with FIR graph filters, our ARMA graph filters show better results for the same number of coefficients.@en