Matched Filtering on Directed Graphs

The matched filter is a crucial concept in both signal analysis and convolutional neural networks (CNNs). Previous work has addressed graph matched filtering principles for undirected graphs. This article expands upon the existing literature, by exploring matched filtering principles for signals on directed graphs. In such cases, the adjacency matrix is asymmetric, and commonly results in nonorthogonal eigenvectors. The presented concept is supported by a detailed analysis and numerical examples.