The Dual Graph Shift Operator: Identifying the Support of the Frequency Domain

Abstract Contemporary data is often supported by an irregular structure, which can be conveniently captured a graph. Accounting for this graph support crucial to analyze the data, leading area known as signal processing (GSP). The two most important tools in GSP are shift operator (GSO), sparse matrix accounting topology of graph, and Fourier transform (GFT), maps signals into frequency domain spanned number graph-related Fourier-like basis vectors. This alternative representation denominated signal. Several attempts have been undertaken order interpret signal, but they all resulted one-dimensional interpretation. However, if original why would simple support? Departing from existing work, we propose coin dual A GSO leads better interpretation its domain, helps understand how different frequencies related clustered, enables development filters filter banks, facilitates generalization classical SP results domain.