Systematic Design of High-Pass Graph Filters via Low-Pass Graph Filters

In traditional signal processing, signals are filtered to obtain information components within time signals by eliminating the noise components. In many applications, towards a similar goal, graph signals used in modeling complex systems need to be filtered appropriately. For this purpose, the field of graph signal processing has emerged by combining traditional signal processing methods and graph theory. Various graph filter definitions and designs have been proposed in the literature, mainly low-pass graph filters. In this study, we propose a systematic method for designing high-pass graph filters using a graph modulation operator together with existing low-pass filters and present simulation examples that include the use of the designed filters in filtering graph signals.