Graph filter designs and implementations

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.