Discrete Linear Canonical Transform on Graphs

TL;DR

This paper introduces the discrete linear canonical transform on graphs (GLCT), extending classical transforms to graph signals, and explores its properties, special cases, and practical examples to demonstrate its effectiveness.

Contribution

It defines the GLCT by integrating graph chirp-Fourier, scale, and fractional Fourier transforms, expanding spectral methods in graph signal processing.

Findings

GLCT generalizes existing graph transforms.

Properties and special cases of GLCT are derived.

Examples show GLCT's effectiveness in graph signal analysis.

Abstract

With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier transform, graph wavelet transform and windowed graph Fourier transform. In this paper, we propose and design the definition of the discrete linear canonical transform on graphs (GLCT), which is an extension of the discrete linear canonical transform (DLCT), just as the graph Fourier transform (GFT) is an extension of the discrete Fourier transform (DFT). First, based on the centrality and scalability of the DLCT eigendecomposition approach, the definition of GLCT is proposed by combining graph chirp-Fourier transform, graph scale transform and graph fractional Fourier transform. Second, we derive and discuss the properties and special cases of GLCT. Finally, some GLCT examples of the graph signals are given to illustrate the improvement of the transformation.