Signal Filtering on Directed Acyclic Graphs

A directed acyclic graph (DAG) is a specialized form of directed graph used extensively for analyzing relationships and dependencies across various domains. However, spectral analysis—a core technique in signal processing on graphs—has been challenging to apply directly to DAGs due to their inherent acyclic structure. In this paper, we introduce a spectral filtering approach for DAGs using graph zero-padding. By adding extra nodes to the DAG, we create a modified graph structure that enables spectral analysis. This new structure supports the application of the graph Fourier transform (GFT) and spectral filtering techniques, enabling spectral filtering while maintaining key aspects of the DAG’s topology and dynamics.